Studia Logica 53 (2):227 - 234 (1994)

Abstract
A BCK-algebra is an algebra in which the terms are generated by a set of variables, 1, and an arrow. We mean by aBCK-identity an equation valid in all BCK-algebras. In this paper using a syntactic method we show that for two termss andt, if neithers=1 nort=1 is a BCK-identity, ands=t is a BCK-identity, then the rightmost variables of the two terms are identical.This theorem was conjectured firstly in [5], and then in [3]. As a corollary of this theorem, we derive that the BCK-algebras do not form a variety, which was originally proved algebraically by Wroski ([4]).
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DOI 10.1007/BF01054710
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Self-Implications in BCI.Tomasz Kowalski - 2008 - Notre Dame Journal of Formal Logic 49 (3):295-305.

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