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Preprint Number 496

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496. Joël Adler
The model companion of the class of pseudocomplemented semilattices is finitely axiomatizable
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Submission date: 14 March 2012.

Abstract:

In this paper it is shown that the class PCSL^{ec} of existentially closed pseudocomplemented semilattices is finitely axiomatizable by appropriately extending the finite axiomatization of the class PCSL^{ac} of algebraically closed pseudocomplemented semilattices presented in Rupp, Addler, and Schmid. Because PCSL^{ec} coincides with the model companion of the class 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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Full text arXiv 1203.3155: pdf, ps.


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