DECIDABILITY AND GODEL INCOMPLETENESS IN AF ¨ C*-ALGEBRAS

• Autor(a) principal: Mundici, Daniele
• Data de Publicação: 2016
• Tipo de documento: Artigo
• Idioma: por
• Título da fonte: Manuscrito (Online)
• Texto Completo: https://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8643903
• topic: MV-algebra. AF C*-algebra. G¨odel incompleteness. Lukasiewicz calculus. Many-valued logic. Decision problem

In the algebraic treatment of quantum statistical systems, the claim “Nature does not have ideals” is sometimes used to convey the idea that the C*-algebras describing natural systems are simple, i.e., they do not have nontrivial homomorphic images. Using our interpretation of AF C*-algebras as algebras of Lukasiewicz calculus, in a previous paper the claim was shown to be incompatible with the existence of a G¨odel incomplete AF C*-algebra for a quantum physical system existing in nature. In this note we survey recent developments on G¨odel incompleteness and decidability issues for AF C*-algebras.