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Free Łukasiewicz implication algebras

By José Patricio Díaz Varela

Abstract

Łukasiewicz implication algebras are the {→,1}-subreducts of MV- algebras. They are the algebraic counterpart of Super-Łukasiewicz Implicational Logics investigated in Komori (Nogoya Math J 72:127-133, 1978). In this paper we give a description of free Łukasiewicz implication algebras in the context of McNaughton functions. More precisely, we show that the |X|-free Łukasiewicz implication algebra is isomorphic to ∪x∈X} [xθ) for a certain congruence θ over the |X|-free MV-algebra. As corollary we describe the free algebras in all subvarieties of Łukasiewicz implication algebras.Fil: Díaz Varela, José Patricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentin

Topics: ŁUKASIEWICZ IMPLICATION ALGEBRAS, FREE ALGEBRAS, MCNAUGHTON FUNCTIONS, MV-ALGEBRAS, WAJSBERG ALGEBRAS, Matemática Aplicada, Matemáticas, CIENCIAS NATURALES Y EXACTAS
Publisher: 'Springer Science and Business Media LLC'
Year: 2008
DOI identifier: 10.1007/s00153-008-0067-5
OAI identifier: oai:ri.conicet.gov.ar:11336/95369
Provided by: CONICET Digital
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