Mathematical Structures: Dense linear orders

# Dense linear orders

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http://mathcs.chapman.edu/structuresold/files/Dense_linear_orders.pdf
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\newtheorem{definition}{Definition}
\newtheorem*{morphisms}{Morphisms}
\newtheorem*{basic_results}{Basic Results}
\newtheorem*{examples}{Examples}
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\newtheorem*{finite_members}{Finite Members}
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\begin{document}
\textbf{\Large Dense linear orders}

\begin{definition}
A \emph{dense linear order} is a \href{Chains.pdf}{Chains} $\mathbf{D}=\langle D,\le\rangle$ such that

$\le$ is \emph{dense}:  $x<y\implies\exists z (x<z$, $z<y)$

Remark:

\end{definition}
\begin{morphisms}
Let $\mathbf{C}$ and $\mathbf{D}$ be dense linear orders. 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 & first-order\\\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 $n$.

$\begin{array}{lr} None \end{array}$
\end{finite_members}
\hyperbaseurl{http://math.chapman.edu/structures/files/}
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\begin{subclasses}\

\href{Dense_linear_orders_without_endpoints.pdf}{Dense linear orders without endpoints}

\end{subclasses}
\begin{superclasses}\

\href{Chains.pdf}{Chains}

\end{superclasses}

\begin{thebibliography}{10}

\bibitem{Ln19xx}

\end{thebibliography}

\end{document}
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