Differences

—		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:
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		+	$x\le y\Longrightarrow h(x)\le h(y)$
		+
		+	====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>
		+	)]
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		+