Abstract

In this work, we attempt to alleviate three equivalent negative results. These are non-axiomatizability of the valid formula schemas of first order logic, non-axiomatizability of any propositional logic equivalent with classical first order logic , and non-axiomatizability of the class of representable cylindric algebras . Here we present two finite schema axiomatizable classes of algebras that contain, as a reduct, the class of representable quasi-polyadic algebras and the class of representable cylindric algebras, respectively. We establish positive results in the direction of finitary algebraization of first order logic without equality as well as that with equality. Finally, we will indicate how these constructions can be applied to turn negative results , above to positive one