Table of Contents

## Directed partial orders

Abbreviation: **DPO**

### Definition

A ** directed partial order** is a poset $\mathbf{P}=\langle P,\leq \rangle $ that is

**, i.e. every finite subset of $P$ has an upper bound in $P$, or equivalently, $P\ne\emptyset$, $\forall xy\exists z (x\le z$ and $y\le z)$.**

*directed*##### Morphisms

Let $\mathbf{P}$ and $\mathbf{Q}$ be directed partial orders. A morphism from $\mathbf{P}$ to $\mathbf{Q}$ is a function $f:Parrow Q$ that is order preserving:

$x\le y\Longrightarrow f(x)\le f(y)$

### Examples

Example 1:

### Basic results

### Properties

Classtype | first-order |
---|---|

Amalgamation property | |

Strong amalgamation property | |

Epimorphisms are surjective |

### Finite members

$\begin{array}{lr} f(1)= &1\\ f(2)= &1\\ f(3)= &2\\ f(4)= &\\ f(5)= &\\ f(6)= &\\ \end{array}$

### Subclasses

### Superclasses

### References

Trace: » directed_partial_orders