Archive for Mathematical Logic 44 (6):763-782 (2005)

Axiomatic set theory with full comprehension is known to be consistent in Łukasiewicz fuzzy predicate logic. But we cannot assume the existence of natural numbers satisfying a simple schema of induction; this extension is shown to be inconsistent.
Keywords Łukasiewicz logic  Fuzzy set theory  Contradiction
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DOI 10.1007/s00153-005-0284-0
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References found in this work BETA

The Liar Paradox and Fuzzy Logic.Petr Hájek, Jeff Paris & John Shepherdson - 2000 - Journal of Symbolic Logic 65 (1):339-346.
The Undecidability of Grisin's Set Theory.Andrea Cantini - 2003 - Studia Logica 74 (3):345 - 368.
Fuzzy Logic and Fuzzy Set Theory.Gaisi Takeuti & Satoko Titani - 1992 - Archive for Mathematical Logic 32 (1):1-32.

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Citations of this work BETA

Logical Consequence and the Paradoxes.Edwin Mares & Francesco Paoli - 2014 - Journal of Philosophical Logic 43 (2-3):439-469.
Paths to Triviality.Tore Øgaard - 2016 - Journal of Philosophical Logic 45 (3):237-276.
Mathematical Fuzzy Logics.Siegfried Gottwald - 2008 - Bulletin of Symbolic Logic 14 (2):210-239.

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