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authorFranciszek Malinka <franciszek.malinka@gmail.com>2022-07-13 23:09:49 +0200
committerFranciszek Malinka <franciszek.malinka@gmail.com>2022-07-13 23:09:49 +0200
commitae1c456f6467a50427fc485ec5ae163495ea0e52 (patch)
tree9232df9cc8d6a218648199dea6d27490d24374cb /sections/fraisse_classes.tex
parent006c57fdeb81d97b1ee222d14346e3844df343f5 (diff)
Ortografia
Diffstat (limited to 'sections/fraisse_classes.tex')
-rw-r--r--sections/fraisse_classes.tex18
1 files changed, 9 insertions, 9 deletions
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 $\delta\colon A\otimes_C B\to A\otimes_C B$