Stone type representation theorems via games


ASLAN KHALİFA T., Khaled M. K. M. I.

Colloquium Mathematicum, vol.155, no.1, pp.141-155, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 155 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.4064/cm7368-1-2018
  • Journal Name: Colloquium Mathematicum
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.141-155
  • Keywords: representability, relation algebras, games and networks
  • Istanbul Medipol University Affiliated: Yes

Abstract

The classes of relativized relation algebras (whose units are not necessarily transitive as binary relations) are known to be finitely axiomatizable. In this article, we give a new proof for this fact that is easier and more transparent than the original proofs. We give direct constructions for all cases, whereas the original proofs reduced the problem to only one case. The proof herein is combinatorial and it uses some techniques from game theory.