  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.
