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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>
		+	)]
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		+
		+
		+
		+