# Differences

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dense_linear_orders [2010/07/29 15:46] (current)
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+=====Dense linear orders=====
+
+====Definition====
+A \emph{dense linear order} is a [[Chains]] $\mathbf{D}=\langle D,\le\rangle$ such that
+
+$\le$ is \emph{dense}:  $x<y\Longrightarrow\exists z (x<z$, $z<y)$
+
+
+Remark:
+
+==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:
+
+$x\le y\Longrightarrow h(x)\le h(y)$
+
+====Examples====
+Example 1:
+
+====Basic results====
+
+
+====Properties====
+^[[Classtype]]  |first-order |
+^[[Quasiequational theory]]  | |
+^[[First-order theory]]  | |
+^[[Amalgamation property]]  | |
+^[[Strong amalgamation property]]  | |
+^[[Epimorphisms are surjective]]  | |
+====Finite members====
+
+$\begin{array}{lr} +None +\end{array}$
+
+====Subclasses====
+[[Dense linear orders without endpoints]]
+
+====Superclasses====
+[[Chains]]
+
+
+====References====
+
+[(Ln19xx>
+)]
+
+
+
+
+