Implicative subreducts of MV-algebras: free and weakly projective objects
In this article, we explore in some detail the free and weakly projective objects of the variety of Łukasiewicz implication algebras (the implicative subreducts of MV-algebras). We review the two already known descriptions of finitely generated free algebras, giving new insights into their structure...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2017 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/64648 |
| Acceso en línea: | http://hdl.handle.net/11336/64648 |
| Access Level: | acceso abierto |
| Palabra clave: | Lukasiewicz Logic Mv-Algebra Implicative Algebra Free Algebra Projective Finitely Presented https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | In this article, we explore in some detail the free and weakly projective objects of the variety of Łukasiewicz implication algebras (the implicative subreducts of MV-algebras). We review the two already known descriptions of finitely generated free algebras, giving new insights into their structure and their connection, as well as providing new proofs of the characterizations. We give a representation theorem for weakly projective algebras as algebras of certain McNaughton functions restricted to rational polyhedra and prove that finitely generated weakly projective algebras coincide with finitely presented ones. We also prove that finite chains are the only totally ordered weakly projective examples in this variety. |
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