The Subalgebra Lattice of A Finite Diagonal–Free Two–Dimensional Cylindric Algebra

Authors

  • Martín Figallo Universidad Nacional del Sur
  • Claudia Monica-Gomes Universidad Nacional de San Juan

DOI:

https://doi.org/10.13053/cys-27-1-4544

Keywords:

Finite Boolean algebras, diagonal–free two–dimensional cylindric algebras, lattice of subalgebras

Abstract

Diagonal–free two–dimensional cylindric algebras (Df2−algebras for short) are Boolean algebras enriched with two existential quantifiers which commute. Df2−algebras were introduced by A. Tarski, L. Chin and F. Thompson with the purpose of providing an algebraic device for the study of the first–order predicate calculus with two variables. This work is devoted to problems related to finite Df2−algebras. More precisely, we study and describe the family of subalgebras of a given finite Df2−algebra. Then, identifying the algebras of this family which are isomorphic, we provide a full description of the lattice of all non–isomorphic subalgebras of a given finite Df2−algebra.

Author Biographies

Martín Figallo, Universidad Nacional del Sur

Instituto de Matematica de Bahía Blanca

Claudia Monica-Gomes, Universidad Nacional de San Juan

Instituto de Ciencias Basicas

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Published

2023-03-30

Issue

Vol. 27 No. 1 (2023): 27(1) 2023

Section

Articles of the Thematic Section (2)

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