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

Marx, M. and Mikulas, Szabolcs (1999) Decidability of cylindric set algebras of dimension two and first-order logic with two variables. The journal of Symbolic Logic 64 (4), pp. 1563-1572. ISSN 0022-4812.

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Official URL: https://doi.org/10.2307/2586797

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.

Metadata

Item Type:	Article
School:	Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
Depositing User:	Sarah Hall
Date Deposited:	13 Jul 2021 14:52
Last Modified:	09 Aug 2023 12:51
URI:	https://eprints.bbk.ac.uk/id/eprint/45085

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