Existentially closed De Morgan algebras

TL;DR

This paper establishes the model completion of the theory of De Morgan algebras, proves its categoricity, and describes definable and algebraic closures, also extending results to Boole-De Morgan algebras.

Contribution

It provides the first axiomatization of the model completion of De Morgan algebras and characterizes their model-theoretic properties, including categoricity and closure operations.

Findings

The theory of De Morgan algebras has a model completion.

The theory is -categorical.

Definable and algebraic closures are characterized.

Abstract

We show that the theory of De Morgan algebras has a model completion and axiomatise it. Then we prove that it is $\aleph_0$-categorical and describe definable and algebraic closures in that theory. We also obtain similar results for Boole-De Morgan algebras.