Differences

This shows you the differences between two versions of the page.

dense_linear_orders [2010/07/29 15:46] (current)
Line 1: Line 1:
 +=====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>
 +)]
 +
 +
 +
 +
 +