Commutative BCK-algebras do not enjoy the interpolation property

Bulletin of the Section of Logic 12 (2):50-53 (1983)
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Abstract

As it has been proved recently by A. Wronski [4] the quasivariety of BCK-algebras enjoys the following interpolation property: If an inequality holds in every BCK-algebra then there exists a term whose variables occur jointly in and in , such that both the inequalities , hold in every BCK-algebra. In this paper we shall show that the interpolation property does not hold for the variety of commutative BCK-algebras

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