We classify every finitely axiomatizable theory in infinite-valued propositional Łukasiewicz logic by an abstract simplicial complex (V,σ) equipped with a weight function ω:V→{1,2,...}. Using the Włodarczyk-Morelli solution of the weak Oda conjecture for toric varieties, we then construct a Turing computable one-one correspondence between (Alexander) equivalence classes of weighted abstract simplicial complexes, and equivalence classes of finitely axiomatizable theories, two theories being equivalent if their Lindenbaum algebras are isomorphic. We discuss the relationship between our classification and Markov's undecidability theorem for PL-homeomorphism of rational polyhedra.

Finite axiomatizability in Łukasiewicz logic / D.Mundici. - In: ANNALS OF PURE AND APPLIED LOGIC. - ISSN 0168-0072. - STAMPA. - 162:(2011), pp. 1035-1047. [10.1016/j.apal.2011.06.026]

Finite axiomatizability in Łukasiewicz logic

MUNDICI, DANIELE
2011

Abstract

We classify every finitely axiomatizable theory in infinite-valued propositional Łukasiewicz logic by an abstract simplicial complex (V,σ) equipped with a weight function ω:V→{1,2,...}. Using the Włodarczyk-Morelli solution of the weak Oda conjecture for toric varieties, we then construct a Turing computable one-one correspondence between (Alexander) equivalence classes of weighted abstract simplicial complexes, and equivalence classes of finitely axiomatizable theories, two theories being equivalent if their Lindenbaum algebras are isomorphic. We discuss the relationship between our classification and Markov's undecidability theorem for PL-homeomorphism of rational polyhedra.
2011
162
1035
1047
D.Mundici
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/537256
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