Stone type representation theorems via games
Volume 155 / 2019
Colloquium Mathematicum 155 (2019), 141-155
MSC: Primary 03G15; Secondary 06E25, 03B45.
DOI: 10.4064/cm7368-1-2018
Published online: 9 November 2018
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.
