A brief history of Tarskian algebraic logic with new perspectives and innovations (Q2193424)

As the author states in his abstract, ``The paper has a survey character but it contains new results and new approaches to old ones (such as the interacion of algebraic logic and descriptive set theory)''. Some of the topics are: Andréka's splitting, giving rise to many non finite axiomatizability results; finite axiomatizability of certain classes of cylindric algebras using the notion of guarding; representabiliy expressed by non-orthodox rules and games; representing all \(CA_n\)'s via twisting set algebras; varieties of representable algebras; connections with descriptive set theory.