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Decidability of cylindric set algebras of dimension two and first-order logic with two variables

Published online by Cambridge University Press:  12 March 2014

Maarten Marx  and
Szabolcs Mikulás
Maarten Marx
Affiliation:
Department of Computing, Imperial College, London, Uk Department of Artificial Intelligence, Faculty of Sciences, Vrije Universiteit Amsterdam, E-mail: marx@cs.vu.nl
Szabolcs Mikulás
Affiliation:
Department of Computer Science, King'S College London, London, UK, E-mail: szabolcs@dcs.kcl.ac.uk
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Abstract

The aim of this paper is to give a new proof for the decidability and finite model property of first-order logic with two variables (without function symbols), using a combinatorial theorem due to Herwig. The results are proved in the framework of polyadic equality set algebras of dimension two (Pse2). The new proof also shows the known results that the universal theory of Pse2 is decidable and that every finite Pse2 can be represented on a finite base. Since the class Cs2 of cylindric set algebras of dimension 2 forms a reduct of Pse2, these results extend to Cs2 as well.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 4 , December 1999 , pp. 1563 - 1572
Copyright
Copyright © Association for Symbolic Logic 1999

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