The countable existentially closed pseudocomplemented semilattice

TL;DR

This paper constructs the unique countable existentially closed pseudocomplemented semilattice, demonstrating its role as the model of the model companion for this algebraic class, using direct limits of algebraically closed structures.

Contribution

It provides the explicit construction of the countable existentially closed pseudocomplemented semilattice as a direct limit, establishing its uniqueness and role as the model of the model companion.

Findings

Existence of a unique countable existentially closed pseudocomplemented semilattice.

Construction via direct limits of algebraically closed structures.

Confirmation of the model companion's properties.

Abstract

As the class of pseudocomplemented semilattices is a universal Horn class generated by a single finite structure it has a $\aleph_0$-categorical model companion. We will construct the countable existentially closed pseudocomplemented semilattice which is the uniquely determined model of cardinality $\aleph_0$ of the model companion as a direct limit of algebraically closed pseudocomplemented semilattices.