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, Volume 35, Issue 1, pp 23–45 | Cite as

Semi-Nelson Algebras

Article

Abstract

Generalizing the well known and exploited relation between Heyting and Nelson algebras to semi-Heyting algebras, we introduce the variety of semi-Nelson algebras. The main tool for its study is the construction given by Vakarelov. Using it, we characterize the lattice of congruences of a semi-Nelson algebra through some of its deductive systems, use this to find the subdirectly irreducible algebras, prove that the variety is arithmetical, has equationally definable principal congruences, has the congruence extension property and describe the semisimple subvarieties.

Keywords

Semi-Heyting algebras Semi-Nelson algebras Twist structures Heyting algebras Nelson algebras 

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© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Instituto de Matemática de Bahía BlancaUniversidad Nacional del Sur-CONICET, Departamento de Matemática -Bahía BlancaArgentina

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