Finite axiomatizability in Łukasiewicz logic

Annals of Pure and Applied Logic 162 (12):1035-1047 (2011)
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Abstract

We classify every finitely axiomatizable theory in infinite-valued propositional Łukasiewicz logic by an abstract simplicial complex equipped with a weight function . Using the Włodarczyk–Morelli solution of the weak Oda conjecture for toric varieties, we then construct a Turing computable one–one correspondence between 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

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References found in this work

On monadic MV-algebras.Antonio Di Nola & Revaz Grigolia - 2004 - Annals of Pure and Applied Logic 128 (1-3):125-139.
Representation theory of MV-algebras.Eduardo J. Dubuc & Yuri A. Poveda - 2010 - Annals of Pure and Applied Logic 161 (8):1024-1046.
Interpretation of De Finetti coherence criterion in Łukasiewicz logic.Daniele Mundici - 2010 - Annals of Pure and Applied Logic 161 (2):235-245.

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