## Journal of Symbolic Logic

### Decidability of Cylindric Set Algebras of Dimension Two and First-Order Logic with Two Variables

#### 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.

#### Article information

Source
J. Symbolic Logic, Volume 64, Issue 4 (1999), 1563-1572.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745938

Mathematical Reviews number (MathSciNet)
MR1780071

Zentralblatt MATH identifier
0953.03012

JSTOR
links.jstor.org

#### Citation

Marx, Maarten; Mikulas, Szabolcs. Decidability of Cylindric Set Algebras of Dimension Two and First-Order Logic with Two Variables. J. Symbolic Logic 64 (1999), no. 4, 1563--1572. https://projecteuclid.org/euclid.jsl/1183745938