A concise guide to finitary and infinitary levels of expressive power of first-order logic

Abstract: In this work, we give a short review of recent results concerning expressive power of first-order logic. We characterize the isomorphism type of the Tarski-Lindenbaum algebra of predicate calculus of a finite rich signature under finitary and infinitary semantic layers of model-theoretic properties. Results presented in this work characterize two levels of expressive power of first-order predicate logic. Author’s statement (just for the reviewer): Currently, a number of absolutely new results is obtained by the author. They characterize expressive power of first-order logic. A few preliminary works have been already published; a few must appear soon; a series of works is prepared for publication. Purpose of this work is to give a short review of used technical methods and basic results in this direction obtained recently by the author.