Bouligand-Severi tangents in MV-algebras

In their recent seminal paper published in the Annals of Pure and Applied Logic, Dubuc and Poveda call an MV-algebra A strongly semisimple if all principal quotients of A are semisimple. All boolean algebras are strongly semisimple, and so are all finitely presented MV-algebras. We show that for any...

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Detalles Bibliográficos
Autores: Busaniche, Manuela, Mundici, Daniele
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2014
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/13885
Acceso en línea:http://hdl.handle.net/11336/13885
Access Level:acceso abierto
Palabra clave:Mv-Algebra
Strongly Semisimple
Bouligand–Severi Tangent
Łukasiewicz Logic
Syntactic And Semantic Consequence
Yosida Frame
Semisimple
Logically Complete Mv-Algebra
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:In their recent seminal paper published in the Annals of Pure and Applied Logic, Dubuc and Poveda call an MV-algebra A strongly semisimple if all principal quotients of A are semisimple. All boolean algebras are strongly semisimple, and so are all finitely presented MV-algebras. We show that for any 1-generator MV-algebra semisimplicity is equivalent to strong semisimplicity. Further, a semisimple 2-generator MV-algebra A is strongly semisimple if and only if its maximal spectral space m(A) does not have any rational Bouligand-Severi tangents at its rational points. In general, when A is finitely generated and m(A) has a Bouligand-Severi tangent then A is not strongly semisimple.