On special implicative filters
by Josep Maria Font
Mathematical Logic Quarterly 45 (1999) 117--126
Abstract
In her well-known book, Rasiowa states without
proof that in implicative algebras there is a one-to-one correspondence
between kernels of epimorphisms and the so-called ``special implicative filters'', and that in the logic whose algebraic counterpart is the class of implicative algebras the deductive filters coincide with the special implicative filters. We show that neither claim is true, and how to repair the situation by redefining some of the notions involved. We answer other questions concerning special implicative filters, taking the theory of algebraizable logics of Blok and Pigozzi as a framework to approach the question in a systematic way.