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

Key words:

• Cylindric algebras
• representability
• games and networks