##
Ildiko Sain, Viktor Gyuris:

#
Finite Schematizable Algebraic Logic

In this work, we attempt to circumvent three (more or less) equivalent
negative results. These are (i) non--axiomatizability (by any finite schema)
of the valid formula schemas of first order logic, (ii) non--axiomatizability
(by finite schema) of any propositional logic equivalent with classical first
order logic (i.e., modal logic of quantification and substitution), and (iii)
non--axiomatizability (by finite schema) of the class of representable
cylindric algebars (i.e, of the algebraic counterpart of first order logic).
Herein, two finite schema axiomatizable classes of algebras are shown that
contain as a reduct the class of representable quasi--polyadic algebras and
the class of representable cylindric algebras, respectively. We present
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 (i),
(ii) above to positive ones.

Retrieve dvi or PostScript version.