On Special Implicative Filters

✍ Scribed by Josep Maria Font

• Book ID: 102942649
• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 630 KB
• Volume: 45
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.19990450111

✦ Synopsis

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 socalled 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.