# Differences

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chains [2010/07/29 15:46] (current)
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+=====Chains=====
+
+====Definition====
+A \emph{chain} is a [[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:
+
+==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:
+
+$x\le y\Longrightarrow h(x)\le h(y)$
+
+====Examples====
+Example 1:
+
+====Basic results====
+
+
+====Properties====
+^[[Classtype]]  |Universal |
+^[[Quasiequational theory]]  | |
+^[[First-order theory]]  | |
+^[[Amalgamation property]]  | |
+^[[Strong amalgamation property]]  | |
+^[[Epimorphisms are surjective]]  | |
+====Finite members====
+
+$\begin{array}{lr} +f(1)= &1\\ +f(2)= &1\\ +f(3)= &1\\ +f(4)= &1\\ +f(5)= &1\\ +f(6)= &1\\ +\end{array}$
+
+====Subclasses====
+[[Well-ordered chains]]
+
+[[Dense linear orders]]
+
+====Superclasses====
+[[Trees]]
+
+
+====References====
+
+[(Ln19xx>
+)]
+
+
+
+
+