## Definition

- A
*partially ordered set (poset)*is a relational structure - A
*strict partially ordered set (strict poset)*is a relational structure ## Basic Results

- Posets and strict posets are definitionally equivalent (Interactive PCP), (complete PCProof)

## Examples

- Any semilattice
- A poset that is not a semilattice: {0<2, 0<3, 1<2, 1<3}

## Decision problems

**Universal Horn Theory**: Decidable**First order theory**: Undecidable## Spectra and growth

**Finite spectrum**:## Subclasses

- semilattices
- trees
- linearly ordered sets
## Expansions

- partially ordered algebraic structures

Adapted from J.Pedersen's Catalogue of Algebraic Systems