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2 Open Mathematics

2 2009

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Topological representation for monadic implication algebras

100%

Abad M. , Cimadamore C. , Díaz Varela J.

Open Mathematics

2009

tom 7

nr 2

299-309

In this paper, every monadic implication algebra is represented as a union of a unique family of monadic filters of a suitable monadic Boolean algebra. Inspired by this representation, we introduce the notion of a monadic implication space, we give a topological representation for monadic implication algebras and we prove a dual equivalence between the category of monadic implication algebras and the category of monadic implication spaces.

Equational spectrum of Hilbert varieties

75%

Padmanabhan R. , Rudeanu S.

Open Mathematics

2009

tom 7

nr 1

66-72

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.