# Existentially Closed Brouwerian Semilattices

## TL;DR

This paper provides a finite, simple axiomatization for the model completion of the variety of Brouwerian semilattices, which are known to be amalgamable and locally finite.

## Contribution

It introduces a concise axiomatization for the existentially closed Brouwerian semilattices' model completion, advancing understanding of their logical structure.

## Key findings

- Model completion exists for Brouwerian semilattices.
- A finite axiomatization is provided for this model completion.
- The axiomatization simplifies the understanding of existentially closed structures.

## Abstract

The variety of Brouwerian semilattices is amalgamable and locally finite, hence by well-known results due to W. H. Wheeler, it has a model completion (whose models are the existentially closed structures). In this paper, we supply for such a model completion a finite and rather simple axiomatization.