Ortografia

3 files changed, 16 insertions, 16 deletions

diff --git a/sections/conj_classes.tex b/sections/conj_classes.tex
index 9620220..c0120d3 100644
--- a/sections/conj_classes.tex
+++ b/sections/conj_classes.tex
@@ -32,7 +32,7 @@
 	We will show that the conjugacy class of $\sigma$ is an intersection of countably
 	many comeagre sets. 
 
-	Let $A_n = \{\alpha\in Aut(M)\mid \alpha\text{ has infinitely many orbits of size }n\}$.
+	Let $A_n = \{\alpha\in \Aut(M)\mid \alpha\text{ has infinitely many orbits of size }n\}$.
 	This set is comeagre for every $n>0$. Indeed, we can represent this set
 	as an intersection of countable family of open dense sets. Let $B_{n,k}$
 	be the set of all finite functions $\beta\colon M\to M$ that consist
@@ -96,7 +96,7 @@
   $\langle \dom(g)\rangle$ and $\langle\rng(g)\rangle$, i.e. substructures 
   generated by $\dom(g)$ and $\rng(g)$ respectively. Of course, in our
   case, $g$ is good
-  if and only if $[g]_{\Aut(\Gamma)} \neq\emptyset$ (becuase of ultrahomogeneity
+  if and only if $[g]_{\Aut(\Gamma)} \neq\emptyset$ (because of ultrahomogeneity
   of $\Gamma$.
 
   Also it is important to mention that an isomorphism between two finitely
@@ -121,7 +121,7 @@
 	words, a basic open set is a set of all extensions of some finite partial
 	automorphism $g_0$ of $\Gamma$. By $B_{g}\subseteq G$ we denote a basic 
 	open subset given by a finite partial isomorphism $g$. Again, Note that $B_g$
-	is nonemty because of ultrahomogeneity of $\Gamma$.
+	is nonempty because of ultrahomogeneity of $\Gamma$.
 
 	With the use of Corollary \ref{corollary:banach-mazur-basis} we can consider 
 	only games where both players choose finite partial isomorphisms. Namely,
@@ -165,7 +165,7 @@
 	$X_{-1} = \emptyset$. 
 	Suppose that player \textit{I} in the $n$-th move chooses a finite partial
 	automorphism $f_n$. We will construct a finite partial automorphism 
-	$g_n\supseteq f_n$ together with a finitely generated substrucutre
+	$g_n\supseteq f_n$ together with a finitely generated substructure
 	$\Gamma_n \subseteq \Gamma$ and a set $X_n\subseteq\bN^2$ 
 	such that the following properties hold:
 
@@ -263,7 +263,7 @@
 	and an embedding $f\colon(A,\alpha)\to(\Gamma,g)$, we may find $n\in\bN$
 	such that $(i,j) = \min\{\{0,1,\ldots n-1\}\times X_{n-1}\}$ and
 	$(A,\alpha) = (A_{i,j},\alpha_{i,j}), (B,\beta)=(B_{i,j},\beta_{i,j})$ and
-	$f = f_{i,j}$. This means that there is a compatbile embedding of $(B,\beta)$ into
+	$f = f_{i,j}$. This means that there is a compatible embedding of $(B,\beta)$ into
 	$(\Gamma_n, g_n)$, which means we can also embed it into $(\Gamma, g)$.
 
 	Hence, $(\Gamma,g)\cong(\Gamma,\sigma)$.
@@ -290,7 +290,7 @@
   Let $\cC$ be a Fraïssé class of finitely generated $L$-structures with
   weak Hrushovski property and canonical amalgamation. 
   Let $\cD$ be the Fraïssé class (by the Theorem \ref{theorem:key-theorem}
-  of the structures of $\cC$ with additional automorphism of the strucutre.
+  of the structures of $\cC$ with additional automorphism of the structure.
   Let $\Gamma = \Flim(\cC)$. 
 
   \begin{proposition}
diff --git a/sections/fraisse_classes.tex b/sections/fraisse_classes.tex
index 993ca73..87647c6 100644
--- a/sections/fraisse_classes.tex
+++ b/sections/fraisse_classes.tex
@@ -15,7 +15,7 @@
   \end{definition}
 
   \begin{definition}
-	We say that a class $\cK$ of finitely generated strcutures 
+	We say that a class $\cK$ of finitely generated structures 
 	is \emph{essentially countable} if it has countably many isomorphism types
 	of finitely generated structures.
   \end{definition}
@@ -40,7 +40,7 @@
   \end{definition}
 
   In terms of category theory we may say that $\cK$ is a category of finitely
-  generated strcutures where morphims are embeddings of those strcutures.
+  generated structures where morphisms are embeddings of those structures.
   Then the above diagram is a \emph{span} diagram in category $\cK$. 
 
   Fraïssé has shown fundamental theorems regarding age of a structure, one of 
@@ -272,7 +272,7 @@
 
   \begin{definition}
 	\label{definition:free_amalgamation} 
-	Let $L$ be a relational language and $\cK$ a class of $L$-strucutres.
+	Let $L$ be a relational language and $\cK$ a class of $L$-structures.
 	$\cK$ has \emph{free amalgamation} if for every
 	$A, B, C\in\cK$ such that $C = A\cap B$ the following diagram commutes:
 	\begin{center}
@@ -283,7 +283,7 @@
 	  \end{tikzcd}
 	\end{center}
 
-	$A\sqcup_C B$ here is an $L$-strcuture with domain $A\cup B$ such that
+	$A\sqcup_C B$ here is an $L$-structure with domain $A\cup B$ such that
 	for every $n$-ary symbol $R$ from $L$, $n$-tuple $\bar{a}\subseteq A\cup B$,
 	we have that $A\sqcup B\models R(\bar{a})$ if and only if [$\bar{a}\subseteq A$ and
 	$A\models R(\bar{a})$] or [$\bar{a}\subseteq B$ and $B\models R(\bar{a})$].
@@ -346,11 +346,11 @@
 	\end{itemize}
   \end{definition}
 
-  From now on in the paper, when $A$ is an $L$-strcuture and $\alpha$ is 
+  From now on in the paper, when $A$ is an $L$-structure and $\alpha$ is 
   an automorphism of
-  $A$, then by $(A, \alpha)$ we mean the strucutre $A$ expanded by the
-  unary function corresping to $\alpha$, and $A$ constantly denotes the
-  $L$-strucutre.
+  $A$, then by $(A, \alpha)$ we mean the structure $A$ expanded by the
+  unary function corresponding to $\alpha$, and $A$ constantly denotes the
+  $L$-structure.
 
   \begin{theorem}
 	\label{theorem:canonical_amalgamation_thm}
@@ -376,7 +376,7 @@
 	\end{center}
 	
 	Then, by the Fact \ref{fact:functor_iso}, $\otimes_C(\eta)$ is an automorphism
-	of the pushout diagram that looks exaclty like the diagram in the second
+	of the pushout diagram that looks exactly like the diagram in the second
 	point of the Definition \ref{definition:canonical_amalgamation}.
 	
 	This means that the morphism $\delta\colon A\otimes_C B\to A\otimes_C B$
diff --git a/sections/preliminaries.tex b/sections/preliminaries.tex
index 2bf254c..0a1b202 100644
--- a/sections/preliminaries.tex
+++ b/sections/preliminaries.tex
@@ -365,7 +365,7 @@
   \begin{proof}
 	Suppose that $\eta_{A}$ is an isomorphism for every $A\in\cC$, where 
 	$\eta_{A}\colon F(A)\to G(A)$ is the morphism of the natural transformation
-	coresponding to $A$. Then $\eta^{-1}$ is simply given by the morphisms
+	corresponding to $A$. Then $\eta^{-1}$ is simply given by the morphisms
 	$\eta^{-1}_A$.
 
 	Now assume that $\eta$ is an isomorphism, i.e. $\eta^{-1}\circ\eta = \id_F$.