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Joël Adler

Publications and source records attributed to Joël Adler.

2 recordsLinked to original sources
arXiv2017

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

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?"

math.LO↗
arXiv2016

The countable existentially closed pseudocomplemented semilattice

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.

math.LO↗