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On Special Implicative Filters
Author(s) -
Font Josep Maria
Publication year - 1999
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19990450111
Subject(s) - mathematics , class (philosophy) , algebra over a field , algebraic number , pure mathematics , computer science , mathematical analysis , artificial intelligence
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.