Decidable and undecidable prime theories in infinite-valued logic

Annals of Pure and Applied Logic 108 (1-3):269-278 (2001)
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Abstract

In classical propositional logic, a theory T is prime iff it is complete. In Łukasiewicz infinite-valued logic the two notions split, completeness being stronger than primeness. Using toric desingularization algorithms and the fine structure of prime ideal spaces of free ℓ -groups, in this paper we shall characterize prime theories in infinite-valued logic. We will show that recursively enumerable prime theories over a finite number of variables are decidable, and we will exhibit an example of an undecidable r.e. prime theory over countably many variables

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Citations of this work

Interpretation of De Finetti coherence criterion in Łukasiewicz logic.Daniele Mundici - 2010 - Annals of Pure and Applied Logic 161 (2):235-245.
Geometry of Robinson consistency in Łukasiewicz logic.Manuela Busaniche & Daniele Mundici - 2007 - Annals of Pure and Applied Logic 147 (1):1-22.
Finite axiomatizability in Łukasiewicz logic.Daniele Mundici - 2011 - Annals of Pure and Applied Logic 162 (12):1035-1047.

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Varieties of MV-algebras.Giovanni Panti - 1999 - Journal of Applied Non-Classical Logics 9 (1):141-157.

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