Komori identities in algebraic logic

• Autorzy: Blok W. , La Falce S.
• Języki publikacji: EN

Abstrakty

EN

A variety generated by a class K of BCK-algebras consists of BCK-algebras if and only if it satisfies a certain kind of identity, first discovered by Komori. A similar phenomenon is shown to hold more generally in a certain class of quasivarieties of logic that includes not only the class of BCK-algebras but also such classes as the quasivariety of biresiduation algebras and quasivarieties of algebras with an equivalence operation. We describe a set of identities (which we call Komori identities), and show that the variety generated by a class K of algebras in one of the quasivarieties considered is contained in the quasivariety if and only it it satisfies a Komori identity. We use the result to establish (i) that the subvarieties of any of the quasivarieties studied are congruence 3-permutable and (ii) that the varietal join of two subvarieties of any of the quasivarieties studied is contained in the quasivariety.

Słowa kluczowe

EN

quasivariety; algebraizable deductive system; equivalence; congruence permutable; lattice of subvarieties

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2000
• Tom: No. 34
• Strony: 79--106

Twórcy

autor

Blok W.

autor

La Falce S.