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Archive for Mathematical Logic

, Volume 56, Issue 3–4, pp 397–402 | Cite as

The countable existentially closed pseudocomplemented semilattice

  • Joël AdlerEmail author
Article

Abstract

As the class \(\mathcal {PCSL}\) of pseudocomplemented semilattices is a universal Horn class generated by a single finite structure it has a \(\aleph _0\)-categorical model companion \(\mathcal {PCSL}^*\). As \(\mathcal {PCSL}\) is inductive the models of \(\mathcal {PCSL}^*\) are exactly the existentially closed models of \(\mathcal {PCSL}\). We will construct the unique existentially closed countable model of \(\mathcal {PCSL}\) as a direct limit of algebraically closed pseudocomplemented semilattices.

Keywords

Existentially closed Pseudocomplemented semilattice Model companion \(\aleph _0\)-categoricity 

Mathematics Subject Classification

03C05 03C10 06D15 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Pädagogische Hochschule BernBernSwitzerland

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