Equational spectrum of Hilbert varieties

• Autorzy: R. Padmanabhan , Sergiu Rudeanu
• Języki publikacji: EN

Abstrakty

EN

We prove that an equational class of Hilbert algebras cannot be defined by a single equation. In particular Hilbert algebras and implication algebras are not one-based. Also, we use a seminal theorem of Alfred Tarski in equational logic to characterize the set of cardinalities of all finite irredundant bases of the varieties of Hilbert algebras, implication algebras and commutative BCK algebras: all these varieties can be defined by independent bases of n elements, for each n > 1.

Słowa kluczowe

EN

Hilbert algebra; Implication algebra; BCK algebra; Equational spectrum; Equational class; One-based theory; Boolean algebra

Kategorie tematyczne

• 06F35: BCK-algebras, BCI-algebras
• 03G25: Other algebras related to logic

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2009
• Tom: 7
• Numer: 1
• Strony: 66-72

Daty

wydano

2009-03-01

online

2009-01-10

Twórcy

autor

R. Padmanabhan

• Department of Mathematics, University of Manitoba, Winnipeg, Canada

autor

Sergiu Rudeanu

• Faculty of Mathematics and Informatics, University of Bucharest, Bucharest, Romania

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-008-0060-6