Chains

http://mathcs.chapman.edu/structuresold/files/Chains.pdf

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\newtheorem*{morphisms}{Morphisms}
\newtheorem*{basic_results}{Basic Results}
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\begin{document}
\textbf{\Large Chains}
\quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Chains}{edit}

\begin{definition}
A \emph{chain} is a \href{Partially_ordered_sets.pdf}{partially ordered set} $\mathbf{C}=\langle C,\le\rangle$ such that


$\le$ is a total order:  $x\le y \mbox{ or } y\le x$


Remark: 

\end{definition}
\begin{morphisms}
Let $\mathbf{C}$ and $\mathbf{D}$ be chains. A morphism from $\mathbf{C}$ to $\mathbf{D}$ is a function $h:C\rightarrow D$ that is a orderpreserving: 

$x\le y\implies h(x)\le h(y)$

\end{morphisms}
\begin{basic_results}
\end{basic_results}
\begin{examples}
\begin{example}
\end{example}
\end{examples}

\begin{table}[h]
\begin{properties} (\href{http://math.chapman.edu/cgi-bin/structures?Properties}{description})

\begin{tabular}{|ll|}\hline
Classtype & Universal\\\hline
Quasiequational theory & \\\hline
First-order theory & \\\hline
Amalgamation property & \\\hline
Strong amalgamation property & \\\hline
Epimorphisms are surjective & \\\hline
\end{tabular}
\end{properties}
\end{table}
\begin{finite_members} $f(n)=$ number of members of size $n$.

$\begin{array}{lr}
f(1)= &1\\
f(2)= &1\\
f(3)= &1\\
f(4)= &1\\
f(5)= &1\\
f(6)= &1\\
\end{array}$
\end{finite_members}
\hyperbaseurl{http://math.chapman.edu/structures/files/}
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\begin{subclasses}\ 

\href{Well-ordered_chains.pdf}{Well-ordered chains} 

\href{Dense_linear_orders.pdf}{Dense linear orders} 

\end{subclasses}
\begin{superclasses}\ 

\href{Trees.pdf}{Trees} 

\end{superclasses}

\begin{thebibliography}{10}

\bibitem{Ln19xx}

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\end{document}
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