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

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

2012-03-14

arxiv.org/abs/1203.3155v1

Mathematics

Logic

Scientific paper

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?"

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