diff --git a/openapi_schema_pydantic/util.py b/openapi_schema_pydantic/util.py
index cb57969..d758e8f 100644
--- a/openapi_schema_pydantic/util.py
+++ b/openapi_schema_pydantic/util.py
@@ -1,5 +1,5 @@
 import logging
-from typing import Any, List, Set, Type, TypeVar
+from typing import Any, Generic, List, Optional, Set, Type, TypeVar
 
 from pydantic import BaseModel
 from pydantic.schema import schema
@@ -12,16 +12,16 @@
 ref_prefix = "#/components/schemas/"
 
 
-class PydanticSchema(Schema):
+class PydanticSchema(Schema, Generic[PydanticType]):
     """Special `Schema` class to indicate a reference from pydantic class"""
 
-    schema_class: Type[PydanticType] = ...
+    schema_class: Type[PydanticType]
     """the class that is used for generate the schema"""
 
 
 def construct_open_api_with_schema_class(
     open_api: OpenAPI,
-    schema_classes: List[Type[PydanticType]] = None,
+    schema_classes: Optional[List[Type[BaseModel]]] = None,
     scan_for_pydantic_schema_reference: bool = True,
     by_alias: bool = True,
 ) -> OpenAPI:
@@ -56,22 +56,22 @@ def construct_open_api_with_schema_class(
         new_open_api.components = Components()
     if new_open_api.components.schemas:
         for existing_key in new_open_api.components.schemas:
-            if existing_key in schema_definitions.get("definitions"):
+            if existing_key in schema_definitions["definitions"]:
                 logger.warning(
                     f'"{existing_key}" already exists in {ref_prefix}. '
                     f'The value of "{ref_prefix}{existing_key}" will be overwritten.'
                 )
         new_open_api.components.schemas.update(
-            {key: Schema.parse_obj(schema_dict) for key, schema_dict in schema_definitions.get("definitions").items()}
+            {key: Schema.parse_obj(schema_dict) for key, schema_dict in schema_definitions["definitions"].items()}
         )
     else:
         new_open_api.components.schemas = {
-            key: Schema.parse_obj(schema_dict) for key, schema_dict in schema_definitions.get("definitions").items()
+            key: Schema.parse_obj(schema_dict) for key, schema_dict in schema_definitions["definitions"].items()
         }
     return new_open_api
 
 
-def _handle_pydantic_schema(open_api: OpenAPI) -> List[Type[PydanticType]]:
+def _handle_pydantic_schema(open_api: OpenAPI) -> List[Type[BaseModel]]:
     """
     This function traverses the `OpenAPI` object and
 
@@ -84,9 +84,9 @@ def _handle_pydantic_schema(open_api: OpenAPI) -> List[Type[PydanticType]]:
     :return: a list of schema classes extracted from `PydanticSchema` objects
     """
 
-    pydantic_types: Set[Type[PydanticType]] = set()
+    pydantic_types: Set[Type[BaseModel]] = set()
 
-    def _traverse(obj: Any):
+    def _traverse(obj: Any) -> None:
         if isinstance(obj, BaseModel):
             fields = obj.__fields_set__
             for field in fields:
@@ -118,7 +118,7 @@ def _traverse(obj: Any):
     return list(pydantic_types)
 
 
-def _construct_ref_obj(pydantic_schema: PydanticSchema):
+def _construct_ref_obj(pydantic_schema: PydanticSchema[PydanticType]) -> Reference:
     ref_obj = Reference(ref=ref_prefix + pydantic_schema.schema_class.__name__)
     logger.debug(f"ref_obj={ref_obj}")
     return ref_obj
diff --git a/openapi_schema_pydantic/v3/v3_0_3/__init__.py b/openapi_schema_pydantic/v3/v3_0_3/__init__.py
index 666664a..1985c6b 100644
--- a/openapi_schema_pydantic/v3/v3_0_3/__init__.py
+++ b/openapi_schema_pydantic/v3/v3_0_3/__init__.py
@@ -6,36 +6,36 @@
 https://github.com/OAI/OpenAPI-Specification/blob/master/versions/3.0.3.md#table-of-contents
 """
 
-from .open_api import OpenAPI
-from .info import Info
-from .contact import Contact
-from .license import License
-from .server import Server
-from .server_variable import ServerVariable
-from .components import Components
-from .paths import Paths
-from .path_item import PathItem
-from .operation import Operation
-from .external_documentation import ExternalDocumentation
-from .parameter import Parameter
-from .request_body import RequestBody
-from .media_type import MediaType
-from .encoding import Encoding
-from .responses import Responses
-from .response import Response
-from .callback import Callback
-from .example import Example
-from .link import Link
-from .header import Header
-from .tag import Tag
-from .reference import Reference
-from .schema import Schema
-from .discriminator import Discriminator
-from .xml import XML
-from .security_scheme import SecurityScheme
-from .oauth_flows import OAuthFlows
-from .oauth_flow import OAuthFlow
-from .security_requirement import SecurityRequirement
+from .open_api import OpenAPI as OpenAPI
+from .info import Info as Info
+from .contact import Contact as Contact
+from .license import License as License
+from .server import Server as Server
+from .server_variable import ServerVariable as ServerVariable
+from .components import Components as Components
+from .paths import Paths as Paths
+from .path_item import PathItem as PathItem
+from .operation import Operation as Operation
+from .external_documentation import ExternalDocumentation as ExternalDocumentation
+from .parameter import Parameter as Parameter
+from .request_body import RequestBody as RequestBody
+from .media_type import MediaType as MediaType
+from .encoding import Encoding as Encoding
+from .responses import Responses as Responses
+from .response import Response as Response
+from .callback import Callback as Callback
+from .example import Example as Example
+from .link import Link as Link
+from .header import Header as Header
+from .tag import Tag as Tag
+from .reference import Reference as Reference
+from .schema import Schema as Schema
+from .discriminator import Discriminator as Discriminator
+from .xml import XML as XML
+from .security_scheme import SecurityScheme as SecurityScheme
+from .oauth_flows import OAuthFlows as OAuthFlows
+from .oauth_flow import OAuthFlow as OAuthFlow
+from .security_requirement import SecurityRequirement as SecurityRequirement
 
 
 # resolve forward references
diff --git a/openapi_schema_pydantic/v3/v3_0_3/callback.py b/openapi_schema_pydantic/v3/v3_0_3/callback.py
index 35bea75..e849bf6 100644
--- a/openapi_schema_pydantic/v3/v3_0_3/callback.py
+++ b/openapi_schema_pydantic/v3/v3_0_3/callback.py
@@ -1,4 +1,7 @@
-from typing import Dict
+from typing import Dict, TYPE_CHECKING
+
+if TYPE_CHECKING:
+    from .path_item import PathItem
 
 
 Callback = Dict[str, "PathItem"]
diff --git a/openapi_schema_pydantic/v3/v3_0_3/discriminator.py b/openapi_schema_pydantic/v3/v3_0_3/discriminator.py
index 699d4ea..525c25b 100644
--- a/openapi_schema_pydantic/v3/v3_0_3/discriminator.py
+++ b/openapi_schema_pydantic/v3/v3_0_3/discriminator.py
@@ -14,7 +14,7 @@ class Discriminator(BaseModel):
     When using the discriminator, _inline_ schemas will not be considered.
     """
 
-    propertyName: str = ...
+    propertyName: str
     """
     **REQUIRED**. The name of the property in the payload that will hold the discriminator value.
     """
diff --git a/openapi_schema_pydantic/v3/v3_0_3/encoding.py b/openapi_schema_pydantic/v3/v3_0_3/encoding.py
index 2821da4..16f2dad 100644
--- a/openapi_schema_pydantic/v3/v3_0_3/encoding.py
+++ b/openapi_schema_pydantic/v3/v3_0_3/encoding.py
@@ -1,9 +1,12 @@
-from typing import Dict, Optional, Union
+from typing import Dict, Optional, TYPE_CHECKING, Union
 
 from pydantic import BaseModel, Extra
 
 from .reference import Reference
 
+if TYPE_CHECKING:
+    from .header import Header
+
 
 class Encoding(BaseModel):
     """A single encoding definition applied to a single schema property."""
diff --git a/openapi_schema_pydantic/v3/v3_0_3/external_documentation.py b/openapi_schema_pydantic/v3/v3_0_3/external_documentation.py
index 599778c..0da41c3 100644
--- a/openapi_schema_pydantic/v3/v3_0_3/external_documentation.py
+++ b/openapi_schema_pydantic/v3/v3_0_3/external_documentation.py
@@ -12,7 +12,7 @@ class ExternalDocumentation(BaseModel):
     [CommonMark syntax](https://spec.commonmark.org/) MAY be used for rich text representation.
     """
 
-    url: AnyUrl = ...
+    url: AnyUrl
     """
     **REQUIRED**. The URL for the target documentation.
     Value MUST be in the format of a URL.
diff --git a/openapi_schema_pydantic/v3/v3_0_3/info.py b/openapi_schema_pydantic/v3/v3_0_3/info.py
index ee12e09..937ba8c 100644
--- a/openapi_schema_pydantic/v3/v3_0_3/info.py
+++ b/openapi_schema_pydantic/v3/v3_0_3/info.py
@@ -13,7 +13,7 @@ class Info(BaseModel):
     and MAY be presented in editing or documentation generation tools for convenience.
     """
 
-    title: str = ...
+    title: str
     """
     **REQUIRED**. The title of the API.
     """
@@ -40,7 +40,7 @@ class Info(BaseModel):
     The license information for the exposed API.
     """
 
-    version: str = ...
+    version: str
     """
     **REQUIRED**. The version of the OpenAPI document
     (which is distinct from the [OpenAPI Specification version](#oasVersion) or the API implementation version).
diff --git a/openapi_schema_pydantic/v3/v3_0_3/license.py b/openapi_schema_pydantic/v3/v3_0_3/license.py
index 29c97ab..e483712 100644
--- a/openapi_schema_pydantic/v3/v3_0_3/license.py
+++ b/openapi_schema_pydantic/v3/v3_0_3/license.py
@@ -8,7 +8,7 @@ class License(BaseModel):
     License information for the exposed API.
     """
 
-    name: str = ...
+    name: str
     """
     **REQUIRED**. The license name used for the API.
     """
diff --git a/openapi_schema_pydantic/v3/v3_0_3/oauth_flow.py b/openapi_schema_pydantic/v3/v3_0_3/oauth_flow.py
index ce76309..37abfb7 100644
--- a/openapi_schema_pydantic/v3/v3_0_3/oauth_flow.py
+++ b/openapi_schema_pydantic/v3/v3_0_3/oauth_flow.py
@@ -27,7 +27,7 @@ class OAuthFlow(BaseModel):
     The URL to be used for obtaining refresh tokens. This MUST be in the form of a URL.
     """
 
-    scopes: Dict[str, str] = ...
+    scopes: Dict[str, str]
     """
     **REQUIRED**. The available scopes for the OAuth2 security scheme.
     A map between the scope name and a short description for it.
diff --git a/openapi_schema_pydantic/v3/v3_0_3/open_api.py b/openapi_schema_pydantic/v3/v3_0_3/open_api.py
index 6b332e8..bcf8cbf 100644
--- a/openapi_schema_pydantic/v3/v3_0_3/open_api.py
+++ b/openapi_schema_pydantic/v3/v3_0_3/open_api.py
@@ -22,7 +22,7 @@ class OpenAPI(BaseModel):
     This is *not* related to the API [`info.version`](#infoVersion) string.
     """
 
-    info: Info = ...
+    info: Info
     """
     **REQUIRED**. Provides metadata about the API. The metadata MAY be used by tooling as required.
     """
@@ -34,7 +34,7 @@ class OpenAPI(BaseModel):
     the default value would be a [Server Object](#serverObject) with a [url](#serverUrl) value of `/`.
     """
 
-    paths: Paths = ...
+    paths: Paths
     """
     **REQUIRED**. The available paths and operations for the API.
     """
diff --git a/openapi_schema_pydantic/v3/v3_0_3/operation.py b/openapi_schema_pydantic/v3/v3_0_3/operation.py
index aa28a44..8917d9d 100644
--- a/openapi_schema_pydantic/v3/v3_0_3/operation.py
+++ b/openapi_schema_pydantic/v3/v3_0_3/operation.py
@@ -66,7 +66,7 @@ class Operation(BaseModel):
     In other cases where the HTTP spec is vague, `requestBody` SHALL be ignored by consumers.
     """
 
-    responses: Responses = ...
+    responses: Responses
     """
     **REQUIRED**. The list of possible responses as they are returned from executing this operation.
     """
diff --git a/openapi_schema_pydantic/v3/v3_0_3/parameter.py b/openapi_schema_pydantic/v3/v3_0_3/parameter.py
index 0f72df3..5b7ab78 100644
--- a/openapi_schema_pydantic/v3/v3_0_3/parameter.py
+++ b/openapi_schema_pydantic/v3/v3_0_3/parameter.py
@@ -17,7 +17,7 @@ class Parameter(BaseModel):
 
     """Fixed Fields"""
 
-    name: str = ...
+    name: str
     """
     **REQUIRED**. The name of the parameter.
     Parameter names are *case sensitive*. 
diff --git a/openapi_schema_pydantic/v3/v3_0_3/request_body.py b/openapi_schema_pydantic/v3/v3_0_3/request_body.py
index 1bf58ce..fe64ab2 100644
--- a/openapi_schema_pydantic/v3/v3_0_3/request_body.py
+++ b/openapi_schema_pydantic/v3/v3_0_3/request_body.py
@@ -16,7 +16,7 @@ class RequestBody(BaseModel):
     [CommonMark syntax](https://spec.commonmark.org/) MAY be used for rich text representation.
     """
 
-    content: Dict[str, MediaType] = ...
+    content: Dict[str, MediaType]
     """
     **REQUIRED**. The content of the request body.
     The key is a media type or [media type range](https://tools.ietf.org/html/rfc7231#appendix-D)
diff --git a/openapi_schema_pydantic/v3/v3_0_3/response.py b/openapi_schema_pydantic/v3/v3_0_3/response.py
index 1f7042c..1a5f135 100644
--- a/openapi_schema_pydantic/v3/v3_0_3/response.py
+++ b/openapi_schema_pydantic/v3/v3_0_3/response.py
@@ -14,7 +14,7 @@ class Response(BaseModel):
     static `links` to operations based on the response.
     """
 
-    description: str = ...
+    description: str
     """
     **REQUIRED**. A short description of the response.
     [CommonMark syntax](https://spec.commonmark.org/) MAY be used for rich text representation.
diff --git a/openapi_schema_pydantic/v3/v3_0_3/security_scheme.py b/openapi_schema_pydantic/v3/v3_0_3/security_scheme.py
index df54c64..a093679 100644
--- a/openapi_schema_pydantic/v3/v3_0_3/security_scheme.py
+++ b/openapi_schema_pydantic/v3/v3_0_3/security_scheme.py
@@ -15,7 +15,7 @@ class SecurityScheme(BaseModel):
     and [OpenID Connect Discovery](https://tools.ietf.org/html/draft-ietf-oauth-discovery-06).
     """
 
-    type: str = ...
+    type: str
     """
     **REQUIRED**. The type of the security scheme.
     Valid values are `"apiKey"`, `"http"`, `"oauth2"`, `"openIdConnect"`.
diff --git a/openapi_schema_pydantic/v3/v3_0_3/server.py b/openapi_schema_pydantic/v3/v3_0_3/server.py
index aeeefd5..4470a2a 100644
--- a/openapi_schema_pydantic/v3/v3_0_3/server.py
+++ b/openapi_schema_pydantic/v3/v3_0_3/server.py
@@ -8,7 +8,7 @@
 class Server(BaseModel):
     """An object representing a Server."""
 
-    url: str = ...
+    url: str
     """
     **REQUIRED**. A URL to the target host.
     
diff --git a/openapi_schema_pydantic/v3/v3_0_3/server_variable.py b/openapi_schema_pydantic/v3/v3_0_3/server_variable.py
index 8808e4a..6bab91c 100644
--- a/openapi_schema_pydantic/v3/v3_0_3/server_variable.py
+++ b/openapi_schema_pydantic/v3/v3_0_3/server_variable.py
@@ -12,7 +12,7 @@ class ServerVariable(BaseModel):
     The array SHOULD NOT be empty.
     """
 
-    default: str = ...
+    default: str
     """
     **REQUIRED**. The default value to use for substitution,
     which SHALL be sent if an alternate value is _not_ supplied.
diff --git a/openapi_schema_pydantic/v3/v3_0_3/tag.py b/openapi_schema_pydantic/v3/v3_0_3/tag.py
index 24e926a..dbb7cc5 100644
--- a/openapi_schema_pydantic/v3/v3_0_3/tag.py
+++ b/openapi_schema_pydantic/v3/v3_0_3/tag.py
@@ -11,7 +11,7 @@ class Tag(BaseModel):
     It is not mandatory to have a Tag Object per tag defined in the Operation Object instances.
     """
 
-    name: str = ...
+    name: str
     """
     **REQUIRED**. The name of the tag.
     """
diff --git a/openapi_schema_pydantic/v3/v3_0_3/util.py b/openapi_schema_pydantic/v3/v3_0_3/util.py
index cb57969..d758e8f 100644
--- a/openapi_schema_pydantic/v3/v3_0_3/util.py
+++ b/openapi_schema_pydantic/v3/v3_0_3/util.py
@@ -1,5 +1,5 @@
 import logging
-from typing import Any, List, Set, Type, TypeVar
+from typing import Any, Generic, List, Optional, Set, Type, TypeVar
 
 from pydantic import BaseModel
 from pydantic.schema import schema
@@ -12,16 +12,16 @@
 ref_prefix = "#/components/schemas/"
 
 
-class PydanticSchema(Schema):
+class PydanticSchema(Schema, Generic[PydanticType]):
     """Special `Schema` class to indicate a reference from pydantic class"""
 
-    schema_class: Type[PydanticType] = ...
+    schema_class: Type[PydanticType]
     """the class that is used for generate the schema"""
 
 
 def construct_open_api_with_schema_class(
     open_api: OpenAPI,
-    schema_classes: List[Type[PydanticType]] = None,
+    schema_classes: Optional[List[Type[BaseModel]]] = None,
     scan_for_pydantic_schema_reference: bool = True,
     by_alias: bool = True,
 ) -> OpenAPI:
@@ -56,22 +56,22 @@ def construct_open_api_with_schema_class(
         new_open_api.components = Components()
     if new_open_api.components.schemas:
         for existing_key in new_open_api.components.schemas:
-            if existing_key in schema_definitions.get("definitions"):
+            if existing_key in schema_definitions["definitions"]:
                 logger.warning(
                     f'"{existing_key}" already exists in {ref_prefix}. '
                     f'The value of "{ref_prefix}{existing_key}" will be overwritten.'
                 )
         new_open_api.components.schemas.update(
-            {key: Schema.parse_obj(schema_dict) for key, schema_dict in schema_definitions.get("definitions").items()}
+            {key: Schema.parse_obj(schema_dict) for key, schema_dict in schema_definitions["definitions"].items()}
         )
     else:
         new_open_api.components.schemas = {
-            key: Schema.parse_obj(schema_dict) for key, schema_dict in schema_definitions.get("definitions").items()
+            key: Schema.parse_obj(schema_dict) for key, schema_dict in schema_definitions["definitions"].items()
         }
     return new_open_api
 
 
-def _handle_pydantic_schema(open_api: OpenAPI) -> List[Type[PydanticType]]:
+def _handle_pydantic_schema(open_api: OpenAPI) -> List[Type[BaseModel]]:
     """
     This function traverses the `OpenAPI` object and
 
@@ -84,9 +84,9 @@ def _handle_pydantic_schema(open_api: OpenAPI) -> List[Type[PydanticType]]:
     :return: a list of schema classes extracted from `PydanticSchema` objects
     """
 
-    pydantic_types: Set[Type[PydanticType]] = set()
+    pydantic_types: Set[Type[BaseModel]] = set()
 
-    def _traverse(obj: Any):
+    def _traverse(obj: Any) -> None:
         if isinstance(obj, BaseModel):
             fields = obj.__fields_set__
             for field in fields:
@@ -118,7 +118,7 @@ def _traverse(obj: Any):
     return list(pydantic_types)
 
 
-def _construct_ref_obj(pydantic_schema: PydanticSchema):
+def _construct_ref_obj(pydantic_schema: PydanticSchema[PydanticType]) -> Reference:
     ref_obj = Reference(ref=ref_prefix + pydantic_schema.schema_class.__name__)
     logger.debug(f"ref_obj={ref_obj}")
     return ref_obj
diff --git a/openapi_schema_pydantic/v3/v3_1_0/__init__.py b/openapi_schema_pydantic/v3/v3_1_0/__init__.py
index dd938d1..bb579fe 100644
--- a/openapi_schema_pydantic/v3/v3_1_0/__init__.py
+++ b/openapi_schema_pydantic/v3/v3_1_0/__init__.py
@@ -6,36 +6,36 @@
 https://github.com/OAI/OpenAPI-Specification/blob/master/versions/3.1.0.md#table-of-contents
 """
 
-from .open_api import OpenAPI
-from .info import Info
-from .contact import Contact
-from .license import License
-from .server import Server
-from .server_variable import ServerVariable
-from .components import Components
-from .paths import Paths
-from .path_item import PathItem
-from .operation import Operation
-from .external_documentation import ExternalDocumentation
-from .parameter import Parameter
-from .request_body import RequestBody
-from .media_type import MediaType
-from .encoding import Encoding
-from .responses import Responses
-from .response import Response
-from .callback import Callback
-from .example import Example
-from .link import Link
-from .header import Header
-from .tag import Tag
-from .reference import Reference
-from .schema import Schema
-from .discriminator import Discriminator
-from .xml import XML
-from .security_scheme import SecurityScheme
-from .oauth_flows import OAuthFlows
-from .oauth_flow import OAuthFlow
-from .security_requirement import SecurityRequirement
+from .open_api import OpenAPI as OpenAPI
+from .info import Info as Info
+from .contact import Contact as Contact
+from .license import License as License
+from .server import Server as Server
+from .server_variable import ServerVariable as ServerVariable
+from .components import Components as Components
+from .paths import Paths as Paths
+from .path_item import PathItem as PathItem
+from .operation import Operation as Operation
+from .external_documentation import ExternalDocumentation as ExternalDocumentation
+from .parameter import Parameter as Parameter
+from .request_body import RequestBody as RequestBody
+from .media_type import MediaType as MediaType
+from .encoding import Encoding as Encoding
+from .responses import Responses as Responses
+from .response import Response as Response
+from .callback import Callback as Callback
+from .example import Example as Example
+from .link import Link as Link
+from .header import Header as Header
+from .tag import Tag as Tag
+from .reference import Reference as Reference
+from .schema import Schema as Schema
+from .discriminator import Discriminator as Discriminator
+from .xml import XML as XML
+from .security_scheme import SecurityScheme as SecurityScheme
+from .oauth_flows import OAuthFlows as OAuthFlows
+from .oauth_flow import OAuthFlow as OAuthFlow
+from .security_requirement import SecurityRequirement as SecurityRequirement
 
 # resolve forward references
 Encoding.update_forward_refs(Header=Header)
diff --git a/openapi_schema_pydantic/v3/v3_1_0/callback.py b/openapi_schema_pydantic/v3/v3_1_0/callback.py
index 254249a..5d71e5c 100644
--- a/openapi_schema_pydantic/v3/v3_1_0/callback.py
+++ b/openapi_schema_pydantic/v3/v3_1_0/callback.py
@@ -1,7 +1,10 @@
-from typing import Dict, Union
+from typing import Dict, TYPE_CHECKING, Union
 
 from .reference import Reference
 
+if TYPE_CHECKING:
+    from .path_item import PathItem
+
 
 Callback = Dict[str, Union["PathItem", Reference]]
 """
diff --git a/openapi_schema_pydantic/v3/v3_1_0/discriminator.py b/openapi_schema_pydantic/v3/v3_1_0/discriminator.py
index 699d4ea..525c25b 100644
--- a/openapi_schema_pydantic/v3/v3_1_0/discriminator.py
+++ b/openapi_schema_pydantic/v3/v3_1_0/discriminator.py
@@ -14,7 +14,7 @@ class Discriminator(BaseModel):
     When using the discriminator, _inline_ schemas will not be considered.
     """
 
-    propertyName: str = ...
+    propertyName: str
     """
     **REQUIRED**. The name of the property in the payload that will hold the discriminator value.
     """
diff --git a/openapi_schema_pydantic/v3/v3_1_0/encoding.py b/openapi_schema_pydantic/v3/v3_1_0/encoding.py
index 7dc6220..0057e46 100644
--- a/openapi_schema_pydantic/v3/v3_1_0/encoding.py
+++ b/openapi_schema_pydantic/v3/v3_1_0/encoding.py
@@ -1,9 +1,12 @@
-from typing import Dict, Optional, Union
+from typing import Dict, Optional, TYPE_CHECKING, Union
 
 from pydantic import BaseModel, Extra
 
 from .reference import Reference
 
+if TYPE_CHECKING:
+    from .header import Header
+
 
 class Encoding(BaseModel):
     """A single encoding definition applied to a single schema property."""
diff --git a/openapi_schema_pydantic/v3/v3_1_0/external_documentation.py b/openapi_schema_pydantic/v3/v3_1_0/external_documentation.py
index 0ce2747..e16eaab 100644
--- a/openapi_schema_pydantic/v3/v3_1_0/external_documentation.py
+++ b/openapi_schema_pydantic/v3/v3_1_0/external_documentation.py
@@ -12,7 +12,7 @@ class ExternalDocumentation(BaseModel):
     [CommonMark syntax](https://spec.commonmark.org/) MAY be used for rich text representation.
     """
 
-    url: AnyUrl = ...
+    url: AnyUrl
     """
     **REQUIRED**. The URL for the target documentation.
     Value MUST be in the form of a URL.
diff --git a/openapi_schema_pydantic/v3/v3_1_0/info.py b/openapi_schema_pydantic/v3/v3_1_0/info.py
index 5e8955b..4c315f6 100644
--- a/openapi_schema_pydantic/v3/v3_1_0/info.py
+++ b/openapi_schema_pydantic/v3/v3_1_0/info.py
@@ -13,7 +13,7 @@ class Info(BaseModel):
     and MAY be presented in editing or documentation generation tools for convenience.
     """
 
-    title: str = ...
+    title: str
     """
     **REQUIRED**. The title of the API.
     """
@@ -45,7 +45,7 @@ class Info(BaseModel):
     The license information for the exposed API.
     """
 
-    version: str = ...
+    version: str
     """
     **REQUIRED**. The version of the OpenAPI document
     (which is distinct from the [OpenAPI Specification version](#oasVersion) or the API implementation version).
diff --git a/openapi_schema_pydantic/v3/v3_1_0/license.py b/openapi_schema_pydantic/v3/v3_1_0/license.py
index f0ba1bb..04c440d 100644
--- a/openapi_schema_pydantic/v3/v3_1_0/license.py
+++ b/openapi_schema_pydantic/v3/v3_1_0/license.py
@@ -8,7 +8,7 @@ class License(BaseModel):
     License information for the exposed API.
     """
 
-    name: str = ...
+    name: str
     """
     **REQUIRED**. The license name used for the API.
     """
diff --git a/openapi_schema_pydantic/v3/v3_1_0/open_api.py b/openapi_schema_pydantic/v3/v3_1_0/open_api.py
index dc1e534..c201d5e 100644
--- a/openapi_schema_pydantic/v3/v3_1_0/open_api.py
+++ b/openapi_schema_pydantic/v3/v3_1_0/open_api.py
@@ -24,7 +24,7 @@ class OpenAPI(BaseModel):
     This is *not* related to the API [`info.version`](#infoVersion) string.
     """
 
-    info: Info = ...
+    info: Info
     """
     **REQUIRED**. Provides metadata about the API. The metadata MAY be used by tooling as required.
     """
diff --git a/openapi_schema_pydantic/v3/v3_1_0/parameter.py b/openapi_schema_pydantic/v3/v3_1_0/parameter.py
index e4f69c4..d34e639 100644
--- a/openapi_schema_pydantic/v3/v3_1_0/parameter.py
+++ b/openapi_schema_pydantic/v3/v3_1_0/parameter.py
@@ -17,7 +17,7 @@ class Parameter(BaseModel):
 
     """Fixed Fields"""
 
-    name: str = ...
+    name: str
     """
     **REQUIRED**. The name of the parameter.
     Parameter names are *case sensitive*. 
diff --git a/openapi_schema_pydantic/v3/v3_1_0/request_body.py b/openapi_schema_pydantic/v3/v3_1_0/request_body.py
index 1bf58ce..fe64ab2 100644
--- a/openapi_schema_pydantic/v3/v3_1_0/request_body.py
+++ b/openapi_schema_pydantic/v3/v3_1_0/request_body.py
@@ -16,7 +16,7 @@ class RequestBody(BaseModel):
     [CommonMark syntax](https://spec.commonmark.org/) MAY be used for rich text representation.
     """
 
-    content: Dict[str, MediaType] = ...
+    content: Dict[str, MediaType]
     """
     **REQUIRED**. The content of the request body.
     The key is a media type or [media type range](https://tools.ietf.org/html/rfc7231#appendix-D)
diff --git a/openapi_schema_pydantic/v3/v3_1_0/response.py b/openapi_schema_pydantic/v3/v3_1_0/response.py
index 1f7042c..1a5f135 100644
--- a/openapi_schema_pydantic/v3/v3_1_0/response.py
+++ b/openapi_schema_pydantic/v3/v3_1_0/response.py
@@ -14,7 +14,7 @@ class Response(BaseModel):
     static `links` to operations based on the response.
     """
 
-    description: str = ...
+    description: str
     """
     **REQUIRED**. A short description of the response.
     [CommonMark syntax](https://spec.commonmark.org/) MAY be used for rich text representation.
diff --git a/openapi_schema_pydantic/v3/v3_1_0/security_scheme.py b/openapi_schema_pydantic/v3/v3_1_0/security_scheme.py
index e1761d0..8f16477 100644
--- a/openapi_schema_pydantic/v3/v3_1_0/security_scheme.py
+++ b/openapi_schema_pydantic/v3/v3_1_0/security_scheme.py
@@ -21,7 +21,7 @@ class SecurityScheme(BaseModel):
     Recommended for most use case is Authorization Code Grant flow with PKCE.
     """
 
-    type: str = ...
+    type: str
     """
     **REQUIRED**. The type of the security scheme.
     Valid values are `"apiKey"`, `"http"`, "mutualTLS", `"oauth2"`, `"openIdConnect"`.
diff --git a/openapi_schema_pydantic/v3/v3_1_0/server.py b/openapi_schema_pydantic/v3/v3_1_0/server.py
index aeeefd5..4470a2a 100644
--- a/openapi_schema_pydantic/v3/v3_1_0/server.py
+++ b/openapi_schema_pydantic/v3/v3_1_0/server.py
@@ -8,7 +8,7 @@
 class Server(BaseModel):
     """An object representing a Server."""
 
-    url: str = ...
+    url: str
     """
     **REQUIRED**. A URL to the target host.
     
diff --git a/openapi_schema_pydantic/v3/v3_1_0/server_variable.py b/openapi_schema_pydantic/v3/v3_1_0/server_variable.py
index ad3d989..ef54cac 100644
--- a/openapi_schema_pydantic/v3/v3_1_0/server_variable.py
+++ b/openapi_schema_pydantic/v3/v3_1_0/server_variable.py
@@ -12,7 +12,7 @@ class ServerVariable(BaseModel):
     The array SHOULD NOT be empty.
     """
 
-    default: str = ...
+    default: str
     """
     **REQUIRED**. The default value to use for substitution,
     which SHALL be sent if an alternate value is _not_ supplied.
diff --git a/openapi_schema_pydantic/v3/v3_1_0/tag.py b/openapi_schema_pydantic/v3/v3_1_0/tag.py
index 24e926a..dbb7cc5 100644
--- a/openapi_schema_pydantic/v3/v3_1_0/tag.py
+++ b/openapi_schema_pydantic/v3/v3_1_0/tag.py
@@ -11,7 +11,7 @@ class Tag(BaseModel):
     It is not mandatory to have a Tag Object per tag defined in the Operation Object instances.
     """
 
-    name: str = ...
+    name: str
     """
     **REQUIRED**. The name of the tag.
     """
diff --git a/pyproject.toml b/pyproject.toml
index 59123ca..8e7d7e3 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -19,3 +19,7 @@ exclude = '''
   )/
 )
 '''
+
+[tool.mypy]
+strict = true
+files = ["openapi_schema_pydantic/", "tests/"]
diff --git a/tests/schema_classes/test_schema.py b/tests/schema_classes/test_schema.py
index 0fd8b8e..2cff6b4 100644
--- a/tests/schema_classes/test_schema.py
+++ b/tests/schema_classes/test_schema.py
@@ -6,7 +6,7 @@
 from openapi_schema_pydantic import Schema, Reference
 
 
-def test_schema():
+def test_schema() -> None:
     schema = Schema.parse_obj(
         {
             "title": "reference list",
@@ -21,7 +21,7 @@ def test_schema():
     assert schema.allOf[0].ref == "#/definitions/TestType"
 
 
-def test_issue_4():
+def test_issue_4() -> None:
     """https://github.com/kuimono/openapi-schema-pydantic/issues/4"""
 
     class TestModel(BaseModel):
diff --git a/tests/schema_classes/test_security_scheme.py b/tests/schema_classes/test_security_scheme.py
index c768dd9..e97f09d 100644
--- a/tests/schema_classes/test_security_scheme.py
+++ b/tests/schema_classes/test_security_scheme.py
@@ -3,7 +3,7 @@
 from openapi_schema_pydantic import SecurityScheme
 
 
-def test_security_scheme_issue_5():
+def test_security_scheme_issue_5() -> None:
     """https://github.com/kuimono/openapi-schema-pydantic/issues/5"""
 
     security_scheme_1 = SecurityScheme(type="openIdConnect", openIdConnectUrl="https://example.com/openIdConnect")
diff --git a/tests/test_alias.py b/tests/test_alias.py
index 2cd0b0f..ea4bca8 100644
--- a/tests/test_alias.py
+++ b/tests/test_alias.py
@@ -1,14 +1,14 @@
 from openapi_schema_pydantic import Header, MediaType, Parameter, PathItem, Reference, Schema, SecurityScheme
 
 
-def test_header_alias():
+def test_header_alias() -> None:
     header_1 = Header(param_in="header")
     header_2 = Header.parse_obj({"param_in": "header"})
     header_3 = Header.parse_obj({"in": "header"})
     assert header_1 == header_2 == header_3
 
 
-def test_media_type_alias():
+def test_media_type_alias() -> None:
     media_type_1 = MediaType(media_type_schema=Schema())
     media_type_2 = MediaType(schema=Schema())
     media_type_3 = MediaType.parse_obj({"media_type_schema": Schema()})
@@ -16,7 +16,7 @@ def test_media_type_alias():
     assert media_type_1 == media_type_2 == media_type_3 == media_type_4
 
 
-def test_parameter_alias():
+def test_parameter_alias() -> None:
     parameter_1 = Parameter(name="test", param_in="path", param_schema=Schema())
     parameter_2 = Parameter(name="test", param_in="path", schema=Schema())
     parameter_3 = Parameter.parse_obj({"name": "test", "param_in": "path", "param_schema": Schema()})
@@ -24,28 +24,28 @@ def test_parameter_alias():
     assert parameter_1 == parameter_2 == parameter_3 == parameter_4
 
 
-def test_path_item_alias():
+def test_path_item_alias() -> None:
     path_item_1 = PathItem(ref="#/dummy")
     path_item_2 = PathItem.parse_obj({"ref": "#/dummy"})
     path_item_3 = PathItem.parse_obj({"$ref": "#/dummy"})
     assert path_item_1 == path_item_2 == path_item_3
 
 
-def test_reference_alias():
+def test_reference_alias() -> None:
     reference_1 = Reference(ref="#/dummy")
     reference_2 = Reference.parse_obj({"ref": "#/dummy"})
     reference_3 = Reference.parse_obj({"$ref": "#/dummy"})
     assert reference_1 == reference_2 == reference_3
 
 
-def test_security_scheme():
+def test_security_scheme() -> None:
     security_scheme_1 = SecurityScheme(type="apiKey", security_scheme_in="header")
     security_scheme_2 = SecurityScheme.parse_obj({"type": "apiKey", "security_scheme_in": "header"})
     security_scheme_3 = SecurityScheme.parse_obj({"type": "apiKey", "in": "header"})
     assert security_scheme_1 == security_scheme_2 == security_scheme_3
 
 
-def test_schema():
+def test_schema() -> None:
     schema_1 = Schema(schema_not=Schema(), schema_format="email")
     schema_2 = Schema.parse_obj({"schema_not": Schema(), "schema_format": "email"})
     schema_3 = Schema.parse_obj({"not": Schema(), "format": "email"})
diff --git a/tests/test_config_example.py b/tests/test_config_example.py
index 29394d4..76f9dc1 100644
--- a/tests/test_config_example.py
+++ b/tests/test_config_example.py
@@ -32,7 +32,7 @@
 )
 
 
-def test_config_example():
+def test_config_example() -> None:
     all_types = [
         OpenAPI,
         Info,
@@ -69,9 +69,11 @@ def test_config_example():
         _assert_config_examples(schema_type)
 
 
-def _assert_config_examples(schema_type):
-    if getattr(schema_type, "Config", None) and getattr(schema_type.Config, "schema_extra", None):
-        examples = schema_type.Config.schema_extra.get("examples")
+def _assert_config_examples(schema_type: object) -> None:
+    Config = getattr(schema_type, "Config", None)
+    schema_extra = getattr(Config, "schema_extra", None)
+    if schema_extra is not None:
+        examples = schema_extra["examples"]
         for example_dict in examples:
-            obj = schema_type(**example_dict)
+            obj = schema_type(**example_dict)  # type: ignore[operator]
             assert obj.__fields_set__
diff --git a/tests/test_example.py b/tests/test_example.py
index 1a2e9a0..9280fd2 100644
--- a/tests/test_example.py
+++ b/tests/test_example.py
@@ -3,7 +3,7 @@
 from openapi_schema_pydantic import Info, OpenAPI, Operation, PathItem, Response
 
 
-def test_readme_example():
+def test_readme_example() -> None:
     open_api_1 = readme_example_1()
     assert open_api_1
     open_api_json_1 = open_api_1.json(by_alias=True, exclude_none=True, indent=2)
diff --git a/tests/test_swagger_openapi_v3.py b/tests/test_swagger_openapi_v3.py
index 86b70f8..759c7f4 100644
--- a/tests/test_swagger_openapi_v3.py
+++ b/tests/test_swagger_openapi_v3.py
@@ -5,7 +5,7 @@
 from openapi_schema_pydantic import OpenAPI, Operation, PathItem
 
 
-def test_swagger_openapi_v3():
+def test_swagger_openapi_v3() -> None:
     open_api = ExtendedOpenAPI.parse_file("tests/data/swagger_openapi_v3.0.1.json")
     assert open_api
 
@@ -31,4 +31,4 @@ class ExtendedPathItem(PathItem):
 
 
 class ExtendedOpenAPI(OpenAPI):
-    paths: Dict[str, ExtendedPathItem] = ...
+    paths: Dict[str, ExtendedPathItem]  # type: ignore[assignment]
diff --git a/tests/util/test_pydantic_field.py b/tests/util/test_pydantic_field.py
index e5e72e9..8b45c24 100644
--- a/tests/util/test_pydantic_field.py
+++ b/tests/util/test_pydantic_field.py
@@ -19,7 +19,7 @@
 from openapi_schema_pydantic.util import PydanticSchema, construct_open_api_with_schema_class
 
 
-def test_pydantic_discriminator_schema_generation():
+def test_pydantic_discriminator_schema_generation() -> None:
     """https://github.com/kuimono/openapi-schema-pydantic/issues/8"""
 
     json_schema = schema([RequestModel])
@@ -56,10 +56,12 @@ def test_pydantic_discriminator_schema_generation():
     }
 
 
-def test_pydantic_discriminator_openapi_generation():
+def test_pydantic_discriminator_openapi_generation() -> None:
     """https://github.com/kuimono/openapi-schema-pydantic/issues/8"""
 
     open_api = construct_open_api_with_schema_class(construct_base_open_api())
+    assert open_api.components is not None
+    assert open_api.components.schemas is not None
     json_schema = open_api.components.schemas["RequestModel"]
     assert json_schema.properties == {
         "data": Schema(
diff --git a/tests/util/test_util.py b/tests/util/test_util.py
index a280106..cba08c0 100644
--- a/tests/util/test_util.py
+++ b/tests/util/test_util.py
@@ -6,7 +6,7 @@
 from openapi_schema_pydantic.util import PydanticSchema, construct_open_api_with_schema_class
 
 
-def test_construct_open_api_with_schema_class_1():
+def test_construct_open_api_with_schema_class_1() -> None:
     open_api = construct_base_open_api_1()
     result_open_api_1 = construct_open_api_with_schema_class(open_api)
     result_open_api_2 = construct_open_api_with_schema_class(open_api, [PingRequest, PingResponse])
@@ -17,7 +17,7 @@ def test_construct_open_api_with_schema_class_1():
     logging.debug(open_api_json)
 
 
-def test_construct_open_api_with_schema_class_2():
+def test_construct_open_api_with_schema_class_2() -> None:
     open_api_1 = construct_base_open_api_1()
     open_api_2 = construct_base_open_api_2()
     result_open_api_1 = construct_open_api_with_schema_class(open_api_1)
@@ -25,11 +25,14 @@ def test_construct_open_api_with_schema_class_2():
     assert result_open_api_1 == result_open_api_2
 
 
-def test_construct_open_api_with_schema_class_3():
+def test_construct_open_api_with_schema_class_3() -> None:
     open_api_3 = construct_base_open_api_3()
 
     result_with_alias_1 = construct_open_api_with_schema_class(open_api_3)
+    assert result_with_alias_1.components is not None
+    assert result_with_alias_1.components.schemas is not None
     schema_with_alias = result_with_alias_1.components.schemas["PongResponse"]
+    assert schema_with_alias.properties is not None
     assert "pong_foo" in schema_with_alias.properties
     assert "pong_bar" in schema_with_alias.properties
 
@@ -37,7 +40,10 @@ def test_construct_open_api_with_schema_class_3():
     assert result_with_alias_1 == result_with_alias_2
 
     result_without_alias = construct_open_api_with_schema_class(open_api_3, by_alias=False)
+    assert result_without_alias.components is not None
+    assert result_without_alias.components.schemas is not None
     schema_without_alias = result_without_alias.components.schemas["PongResponse"]
+    assert schema_without_alias.properties is not None
     assert "resp_foo" in schema_without_alias.properties
     assert "resp_bar" in schema_without_alias.properties
 
diff --git a/tests/v3_0_3/test_config_example.py b/tests/v3_0_3/test_config_example.py
index 2fb3f16..d882b40 100644
--- a/tests/v3_0_3/test_config_example.py
+++ b/tests/v3_0_3/test_config_example.py
@@ -32,7 +32,7 @@
 )
 
 
-def test_config_example():
+def test_config_example() -> None:
     all_types = [
         OpenAPI,
         Info,
@@ -69,9 +69,11 @@ def test_config_example():
         _assert_config_examples(schema_type)
 
 
-def _assert_config_examples(schema_type):
-    if getattr(schema_type, "Config", None) and getattr(schema_type.Config, "schema_extra", None):
-        examples = schema_type.Config.schema_extra.get("examples")
+def _assert_config_examples(schema_type: object) -> None:
+    Config = getattr(schema_type, "Config", None)
+    schema_extra = getattr(Config, "schema_extra", None)
+    if schema_extra is not None:
+        examples = schema_extra.get("examples")
         for example_dict in examples:
-            obj = schema_type(**example_dict)
+            obj = schema_type(**example_dict)  # type: ignore[operator]
             assert obj.__fields_set__
diff --git a/tests/v3_0_3/test_util.py b/tests/v3_0_3/test_util.py
index 8193726..97a5a29 100644
--- a/tests/v3_0_3/test_util.py
+++ b/tests/v3_0_3/test_util.py
@@ -11,11 +11,12 @@
     Reference,
     RequestBody,
     Response,
+    Schema,
 )
 from openapi_schema_pydantic.v3.v3_0_3.util import PydanticSchema, construct_open_api_with_schema_class
 
 
-def test_construct_open_api_with_schema_class_1():
+def test_construct_open_api_with_schema_class_1() -> None:
     open_api = construct_base_open_api_1()
     result_open_api_1 = construct_open_api_with_schema_class(open_api)
     result_open_api_2 = construct_open_api_with_schema_class(open_api, [PingRequest, PingResponse])
@@ -26,7 +27,7 @@ def test_construct_open_api_with_schema_class_1():
     logging.debug(open_api_json)
 
 
-def test_construct_open_api_with_schema_class_2():
+def test_construct_open_api_with_schema_class_2() -> None:
     open_api_1 = construct_base_open_api_1()
     open_api_2 = construct_base_open_api_2()
     result_open_api_1 = construct_open_api_with_schema_class(open_api_1)
@@ -34,11 +35,15 @@ def test_construct_open_api_with_schema_class_2():
     assert result_open_api_1 == result_open_api_2
 
 
-def test_construct_open_api_with_schema_class_3():
+def test_construct_open_api_with_schema_class_3() -> None:
     open_api_3 = construct_base_open_api_3()
 
     result_with_alias_1 = construct_open_api_with_schema_class(open_api_3)
+    assert result_with_alias_1.components is not None
+    assert result_with_alias_1.components.schemas is not None
     schema_with_alias = result_with_alias_1.components.schemas["PongResponse"]
+    assert isinstance(schema_with_alias, Schema)
+    assert schema_with_alias.properties is not None
     assert "pong_foo" in schema_with_alias.properties
     assert "pong_bar" in schema_with_alias.properties
 
@@ -46,7 +51,11 @@ def test_construct_open_api_with_schema_class_3():
     assert result_with_alias_1 == result_with_alias_2
 
     result_without_alias = construct_open_api_with_schema_class(open_api_3, by_alias=False)
+    assert result_without_alias.components is not None
+    assert result_without_alias.components.schemas is not None
     schema_without_alias = result_without_alias.components.schemas["PongResponse"]
+    assert isinstance(schema_without_alias, Schema)
+    assert schema_without_alias.properties is not None
     assert "resp_foo" in schema_without_alias.properties
     assert "resp_bar" in schema_without_alias.properties
 
diff --git a/tests/v3_1_0/__init__.py b/tests/v3_1_0/__init__.py
index df2a9c0..f0cbec1 100644
--- a/tests/v3_1_0/__init__.py
+++ b/tests/v3_1_0/__init__.py
@@ -1,6 +1,6 @@
 from openapi_schema_pydantic.v3.v3_1_0.schema import Schema
 
 
-def test_empty_schema():
+def test_empty_schema() -> None:
     schema = Schema.parse_obj({})
     assert schema == Schema()