Tarskian Algebraic Logic
by
Tarek Sayed Ahmed
University of Cairo, Egypt

This is a survey talk on algebraic logic. It gives a historical background leading up to a modern perspective. Central problems in algebraic logic (like the representation problem) are discussed in connection to other branches of logic, like modal logic, proof theory, model-theoretic forcing and Godel's incompleteness results. Several open problems are posed. We focus on cylindric algebras which are natural algebras of n-ary relations. Relation algebras (which are algebras of binary relation) are mostly only covered insofar as they relate to cylindric algebras. Cylindric and relation algebras were introduced by Tarski, hence the title of the talk.

Date received: July 8, 2005