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A glimpse of deductive systems in algebra

Dumitru Buşneag, Sergiu Rudeanu (2010)

Open Mathematics

The concept of a deductive system has been intensively studied in algebraic logic, per se and in connection with various types of filters. In this paper we introduce an axiomatization which shows how several resembling theorems that had been separately proved for various algebras of logic can be given unique proofs within this axiomatic framework. We thus recapture theorems already known in the literature, as well as new ones. As a by-product we introduce the class of pre-BCK algebras.

A groupoid characterization of Boolean algebras

Ivan Chajda (2004)

Discussiones Mathematicae - General Algebra and Applications

We present a groupoid which can be converted into a Boolean algebra with respect to term operations. Also conversely, every Boolean algebra can be reached in this way.

A metrizable completely regular ordered space

Hans-Peter A. Künzi, Stephen W. Watson (1994)

Commentationes Mathematicae Universitatis Carolinae

We construct a completely regular ordered space ( X , 𝒯 , ≤ ) such that X is an I -space, the topology 𝒯 of X is metrizable and the bitopological space ( X , 𝒯 ♯ , 𝒯 ♭ ) is pairwise regular, but not pairwise completely regular. (Here 𝒯 ♯ denotes the upper topology and 𝒯 ♭ the lower topology of X .)

A non commutative generalization of ☆ -autonomous lattices

P. Emanovský, Jiří Rachůnek (2008)

Czechoslovak Mathematical Journal

Pseudo ☆ -autonomous lattices are non-commutative generalizations of ☆ -autonomous lattices. It is proved that the class of pseudo ☆ -autonomous lattices is a variety of algebras which is term equivalent to the class of dualizing residuated lattices. It is shown that the kernels of congruences of pseudo ☆ -autonomous lattices can be described as their normal ideals.

A note on good pseudo BL-algebras

Magdalena Wojciechowska-Rysiawa (2010)

Discussiones Mathematicae - General Algebra and Applications

Pseudo BL-algebras are a noncommutative extention of BL-algebras. In this paper we study good pseudo BL-algebras and consider some classes of these algebras.

A note on noninterpretability in o-minimal structures

Ricardo Bianconi (1998)

Fundamenta Mathematicae

We prove that if M is an o-minimal structure whose underlying order is dense then Th(M) does not interpret the theory of an infinite discretely ordered structure. We also make a conjecture concerning the class of the theory of an infinite discretely ordered o-minimal structure.

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