dense_linear_orders - MathStructures

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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>
)]

Trace: • finite_integral_ordered_monoids • distributive_p-algebras • cylindric_algebras • residual_size

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