Table of Contents
Dense linear orders
Definition
A dense linear order is a Chains $\mathbf{D}=\langle D,\le\rangle$ such that
$\le$ is 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
Superclasses
References
Trace: » dense_linear_orders