Table of Contents
Chains
Definition
A 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:
$x\le y\Longrightarrow h(x)\le h(y)$
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
Superclasses
References
Trace: » chains