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

Journal of Symbolic Logic 64 (4):1563-1572 (1999)
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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 (Pse 2 ). The new proof also shows the known results that the universal theory of Pse 2 is decidable and that every finite Pse 2 can be represented on a finite base. Since the class Cs 2 of cylindric set algebras of dimension 2 forms a reduct of Pse 2 , these results extend to Cs 2 as well

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References found in this work

Two-dimensional modal logic.Krister Segerberg - 1973 - Journal of Philosophical Logic 2 (1):77 - 96.
On languages with two variables.Michael Mortimer - 1975 - Mathematical Logic Quarterly 21 (1):135-140.

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