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DECIDABILITY AND GODEL INCOMPLETENESS IN AF ¨ C*-ALGEBRAS
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MV-algebra. AF C*-algebra. G¨odel incompleteness. Lukasiewicz calculus. Many-valued logic. Decision problem

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MUNDICI, Daniele. DECIDABILITY AND GODEL INCOMPLETENESS IN AF ¨ C*-ALGEBRAS. Manuscrito: Revista Internacional de Filosofia, Campinas, SP, v. 28, n. 2, p. 547–558, 2016. Disponível em: https://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8643903. Acesso em: 20 jun. 2024.

Resumo

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.
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