On Special Implicative Filters

Mathematical Logic Quarterly 45 (1):117-126 (1999)
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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

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Citations of this work

Preface.Matteo Pascucci & Adam Tamas Tuboly - 2019 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 26 (3):318-322.

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References found in this work

An Algebraic Approach to Non-Classical Logics.Helena Rasiowa - 1974 - Amsterdam, Netherlands: Warszawa, Pwn - Polish Scientific Publishers.
Equivalential logics (I).Janusz Czelakowski - 1981 - Studia Logica 40 (3):227 - 236.
Algebraizable Logics.W. J. Blok & Don Pigozzi - 2014 - Advanced Reasoning Forum.
Equivalential logics.Janusz Czelakowski - 1981 - Studia Logica 40 (3):227-236.
Sur les Algèbres de Hilbert.Antonio Diego, Jean Porte & Luisa Iturrioz - 1970 - Journal of Symbolic Logic 35 (1):139-139.

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