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Topological representation for implication algebras

By Manuel Abad, José Patricio Díaz Varela and Antoni Torrens

Abstract

In this paper we give a description of an implication algebra A as a union of a unique family of filters of a suitable Boolean algebra Bo(A), called the Boolean closure of A. From this representation we obtain a notion of topological implication space and we give a dual equivalence based in the Stone representation for Boolean algebras. As an application we provide the implication space of all free implication algebras.Fil: Abad, Manuel. Universidad Nacional del Sur. Departamento de Matemática; ArgentinaFil: 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; ArgentinaFil: Torrens, Antoni. Universidad de Barcelona; Españ

Topics: BOOLEAN ALGEBRAS, BOOLEAN SPACES, DUAL CATEGORICAL EQUIVALENCE, IMPLICATION ALGEBRAS, IMPLICATION SPACES, Matemática Aplicada, Matemáticas, CIENCIAS NATURALES Y EXACTAS
Publisher: 'Springer Science and Business Media LLC'
Year: 2004
DOI identifier: 10.1007/s00012-004-1872-2
OAI identifier: oai:ri.conicet.gov.ar:11336/95363
Provided by: CONICET Digital
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