The countable existentially closed pseudocomplemented semilattice |
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Authors: | Joël Adler |
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Institution: | 1.P?dagogische Hochschule Bern,Bern,Switzerland |
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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. |
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