Effectiveness in RPL, with applications to continuous logic

Annals of Pure and Applied Logic 161 (6):789-799 (2010)
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Abstract

In this paper, we introduce a foundation for computable model theory of rational Pavelka logic and continuous logic, and prove effective versions of some related theorems in model theory. We show how to reduce continuous logic to rational Pavelka logic. We also define notions of computability and decidability of a model for logics with computable, but uncountable, set of truth values; we show that provability degree of a formula with respect to a linear theory is computable, and use this to carry out an effective Henkin construction. Therefore, for any effectively given consistent linear theory in continuous logic, we effectively produce its decidable model. This is the best possible, since we show that the computable model theory of continuous logic is an extension of computable model theory of classical logic. We conclude with noting that the unique separable model of a separably categorical and computably axiomatizable theory is decidable

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Author's Profile

Farzad Didehvar
Amir Kabir University University (Tehran Polytechnic)

References found in this work

Metamathematics of Fuzzy Logic.Petr Hájek - 1998 - Dordrecht, Boston and London: Kluwer Academic Publishers.
Model theoretic forcing in analysis.Itaï Ben Yaacov & José Iovino - 2009 - Annals of Pure and Applied Logic 158 (3):163-174.
Foundations of Constructive Mathematics.Michael J. Beeson - 1987 - Studia Logica 46 (4):398-399.
Domain representability of metric spaces.Jens Blanck - 1997 - Annals of Pure and Applied Logic 83 (3):225-247.

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