Partially Ordered Sets

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

PCP: Point and Click Proofs, Peter Jipsen, 2001

Definition