Geometrical representation theorems for cylindric-type algebras

Khaled M. K. M. I., Sayed Ahmed T.

QUAESTIONES MATHEMATICAE, vol.43, no.1, pp.81-96, 2020 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.2989/16073606.2018.1538063
  • Journal Name: QUAESTIONES MATHEMATICAE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.81-96
  • Keywords: Cylindric algebras, representability, games and networks
  • Istanbul Medipol University Affiliated: No

Abstract

In this paper, we give new proofs of the celebrated Andréka-Resek-Thompson representability results of certain axiomatized cylindric-like algebras. Such representability results provide completeness theorems for variants of first order logic, that can also be viewed as multi-modal logics. The proofs herein are combinatorial and we also use some techniques from game theory.