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Finitely axiomatizable varieties of BCK-algebras. (English) Zbl 0567.08006

The main theorem of the paper is that the join of two relatively finitely axiomatizable subvarieties of a variety of expanded BCK-algebras is also finitely axiomatizable relative to the variety. The notion of a variety of expanded BCK-algebras, introduced in the paper, encompasses various varieties as examples, e.g. the variety of commutative complementary semigroups of Bosbach, the one of the Heyting algebras and the one of the MV-algebras of Chang.
Reviewer: H.Yutani

MSC:

08B05 Equational logic, Mal’tsev conditions
06F15 Ordered groups
03G25 Other algebras related to logic
08B15 Lattices of varieties
06D20 Heyting algebras (lattice-theoretic aspects)
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References:

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