The countable existentially closed pseudocomplemented semilattice

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.