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On arithmetic in the Cantor- Łukasiewicz fuzzy set theory
Archive for Mathematical Logic 44 (6):763-782 (2005)
Abstract
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.My notes
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Citations of this work
Logical Consequence and the Paradoxes.Edwin Mares & Francesco Paoli - 2014 - Journal of Philosophical Logic 43 (2-3):439-469.
Universes of Fuzzy Sets and Axiomatizations of Fuzzy Set Theory. Part I: Model-Based and Axiomatic Approaches.Siegfried Gottwald - 2006 - Studia Logica 82 (2):211-244.
Distinguishing non-standard natural numbers in a set theory within Łukasiewicz logic.Shunsuke Yatabe - 2007 - Archive for Mathematical Logic 46 (3-4):281-287.
References found in this work
Intuitionistic fuzzy logic and intuitionistic fuzzy set theory.Gaisi Takeuti & Satoko Titani - 1984 - Journal of Symbolic Logic 49 (3):851-866.
The consistency of the axiom of comprehension in the infinite-valued predicate logic of łukasiewicz.Richard B. White - 1979 - Journal of Philosophical Logic 8 (1):509 - 534.
The liar paradox and fuzzy logic.Petr Hájek, Jeff Paris & John Shepherdson - 2000 - Journal of Symbolic Logic 65 (1):339-346.
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