Amalgamation in finite dimensional cylindric algebras |
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Authors: | M Marx |
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Institution: | (1) Institute for Logic, Language and Computation, CCSOM, Universiteit van Amsterdam, Plantage Muidergracht 24, NL-1018 TV Amsterdam, The Netherlands, e-mail: marx@wins.uva.nl (http:// www.wins.uva.nl), NL;(2) Department of Computing, Imperial College, 180 Queen's Gate SW7 2BZ, London, UK, GB |
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Abstract: | For every finite n > 1, the embedding property fails in the class of all n-dimensional cylindric type algebras which satisfy the following. Their boolean reducts are boolean algebras and two of the
cylindrifications are normal, additive and commute. This result also holds for all subclasses containing the representable
n-dimensional cylindric algebras. This considerably strengthens a result of S. Comer on CA
n
and provides a strong counterexample for interpolation in finite variable fragments of first order logic. We provide a new
modern proof, using an argument inspired by modal logic.
February 22, 1999. |
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Keywords: | and phrases: Cylindric algebras amalgamation interpolation |
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