Geometrical representation theorems for cylindric-type algebras

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.

Mathematics Subject Classification (2010): Primary 03G15; Secondary 03G25, 03B45.

Keywords: Cylindric algebras, representability, games and networks