Recursive axiomatizations for representable posets

TL;DR

This paper develops explicit first-order axiomatizations for classes of posets that can be represented as systems of sets with order given by inclusion, focusing on existing meets and joins of specific countable sizes.

Contribution

It introduces recursive axiomatizations for representable posets using model theoretic techniques, advancing the understanding of their logical characterization.

Findings

Provides explicit first-order axioms for representable posets

Uses model theoretic methods to construct axiomatizations

Focuses on countable cardinalities of meets and joins

Abstract

We use model theoretic techniques to construct explicit first-order axiomatizations for the classes of posets that can be represented as systems of sets, where the order relation is given by inclusion, and existing meets and joins of specified countable cardinalities correspond to intersections and unions respectively.