Axiomatizability of reducts of algebras of relations |
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Authors: | Ian Hodkinson Szabolcs Mikulás |
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Affiliation: | (1) Department of Computing Imperial College, London, UK, e-mail: imh@doc.ic.ac.uk, GB;(2) Department of Computer Science King's College, London, UK, e-mail: szabolcs@dcs.kcl.ac.uk, GB;(3) Department of Computer Science, Birkbeck College, London, UK, e-mail: szabdcs@dcs.bbk.ac.uk, GB |
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Abstract: | In this paper, we prove that any subreduct of the class of representable relation algebras whose similarity type includes intersection, relation composition and converse is a non-finitely axiomatizable quasivariety and that its equational theory is not finitely based. We show the same result for subreducts of the class of representable cylindric algebras of dimension at least three whose similarity types include intersection and cylindrifications. A similar result is proved for subreducts of the class of representable sequential algebras. Received October 7, 1998; accepted in final form September 10, 1999. |
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