The model companion of the class of pseudocomplemented semilattices is finitely axiomatizable

Abstract

In this paper it is shown that the class $\mathcal{PCSL}^{ec}$ of existentially closed pseudocomplemented semilattices is finitely axiomatizable by appropriately extending the finite axiomatization of the class $\mathcal{\mathcal{PCSL}}^{ac}$ of algebraically closed pseudocomplemented semilattices presented in Rupp, Addler, and Schmid. Because $\mathcal{PCSL}^{ec}$ coincides with the model companion of the class $\mathcal{PCSL}$ of pseudocomplemented semilattices this addendum to Rupp, Addler, and Schmid solves the problem posed by Albert and Burris in the final paragraph of their paper: "Does the class of pseudocomplemented semilattices have a finitely axiomatizable model companion?"