Fix typos (#332)

* fix typos

* revert erroneous change

Author: vladh

content/incompleteness/arithmetization-syntax/coding-symbols.tex

@@ -95,7 +95,7 @@
     c_0},\scode{)}}.
 \]
 Here, $\scode{\eq}$ is $\tuple{0,7} = 2^{0+1}\cdot
-3^{7=1}$, $\scode{\Obj v_0}$ is $\tuple{1,0} = 2^{1+1}\cdot3^{0+1}$,
+3^{7+1}$, $\scode{\Obj v_0}$ is $\tuple{1,0} = 2^{1+1}\cdot3^{0+1}$,
 etc. So $\Gn{=(\Obj v_0,\Obj c_0)}$ is
 \begin{multline*}
 2^{\scode{=} + 1}\cdot 3^{\scode{(}+1}\cdot 5^{\scode{\Obj v_0}+1}

content/incompleteness/introduction/definitions.tex

@@ -223,7 +223,7 @@
 $y_1$, \dots, $y_n$ are all the free variables of~$!A$ and the initial
 quantifiers of~$!B$ bind the variables~$y_1$, \dots,~$y_n$.  Once we
 have extracted this~$!A$ and checked that its free variables match the
-variables bound by the universal qauntifiers at the front
+variables bound by the universal quantifiers at the front
 and~$\lforall[x]$, we go on to check that the antecedent of the
 conditional matches
 \[

content/incompleteness/introduction/historical-background.tex

@@ -33,7 +33,7 @@
 thorough and systematic study of the syllogism.
 
 Aristotle's logic dominated scholastic philosophy through the middle
-ages; indeed, as late as eighteenth century Kant maintained that
+ages; indeed, as late as the eighteenth century, Kant maintained that
 Aristotle's logic was perfect and in no need of revision. But the
 theory of the syllogism is far too limited to model anything but
 the most superficial aspects of mathematical reasoning. A century
@@ -71,7 +71,7 @@
 Greeks. Euclid's \emph{Elements}, written around 300 B.C., is already
 a mature representative of Greek mathematics, with its emphasis on
 rigor and precision. The definitions and proofs in Euclid's
-\emph{Elements} survive more or less in tact in high school geometry
+\emph{Elements} survive more or less intact in high school geometry
 textbooks today (to the extent that geometry is still taught in high
 schools). This model of mathematical reasoning has been held to be a
 paradigm for rigorous argumentation not only in mathematics but in

content/incompleteness/introduction/undecidability.tex

@@ -62,7 +62,7 @@
 relations; this means that all theories that include $\Th{Q}$, such as
 $\Th{PA}$ and $\Th{TA}$, also do, and hence also are not
 !!{decidable}. (Since all these theories are true in the standard
-model, they are all consistent.))
+model, they are all consistent.)
 
 We can also use this result to obtain a weak version of the first
 incompleteness theorem.  Any theory that is !!{axiomatizable} and