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- Publisher
- de Gruyter
- Copyright
- Copyright © 2009 by the
- ISSN
- 2391-5455
- eISSN
- 2391-5455
- DOI
- 10.2478/s11533-008-0060-6
- Publisher site
- See Article on Publisher Site
Abstract
Abstract 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.
Journal
Open Mathematics – de Gruyter
Published: Mar 1, 2009