Axiomatisability problems for <Emphasis Type="Italic">S</Emphasis>-posets |
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Authors: | Victoria Gould Lubna Shaheen |
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Institution: | (3) Dept. Computer Sci., Florida State Univ., Tallahassee, Florida 32308-4530, USA |
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Abstract: | Let \(\mathcal{C}\) be a class of ordered algebras of a given fixed type τ. Associated with the type is a first order language L τ , which must also contain a binary predicate to be interpreted by the ordering in members of \(\mathcal{C}\). One can then ask the question, when is the class \(\mathcal{C}\) axiomatisable by sentences of L τ ? In this paper we will be considering axiomatisability problems for classes of left S-posets over a pomonoid S (that is, a monoid S equipped with a partial order compatible with the binary operation). We aim to determine the pomonoids S such that certain categorically defined classes are axiomatisable. The classes we consider are the free S-posets, the projective S-posets and classes arising from flatness properties. Some of these cases have been studied in a recent article by Pervukhin and Stepanova. We present some general strategies to determine axiomatisability, from which their results for the classes of weakly po-flat and po-flat S-posets will follow. We also consider a number of classes not previously examined. |
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