Displaying similar documents to “Some properties of epimorphisms of Hilbert algebras”

Representation and duality for Hilbert algebras

Sergio Celani, Leonardo Cabrer, Daniela Montangie (2009)

Open Mathematics

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In this paper we introduce a special kind of ordered topological spaces, called Hilbert spaces. We prove that the category of Hilbert algebras with semi-homomorphisms is dually equivalent to the category of Hilbert spaces with certain relations. We restrict this result to give a duality for the category of Hilbert algebras with homomorphisms. We apply these results to prove that the lattice of the deductive systems of a Hilbert algebra and the lattice of open subsets of its dual Hilbert...

Equational spectrum of Hilbert varieties

R. Padmanabhan, Sergiu Rudeanu (2009)

Open Mathematics

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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. ...

Remarks on commutative Hilbert algebras

Radomír Halaš (2002)

Mathematica Bohemica

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The paper shows that commutative Hilbert algebras introduced by Y. B. Jun are just J. C. Abbot’s implication algebras.