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On arithmetic in the Cantor- Łukasiewicz fuzzy set theory

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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.

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  1. Institute of Computer Science, Academy of Sciences of the Czech Republic, 182 07 Prague, Czech Republic

    Petr Hájek

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  1. Petr Hájek
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Additional information

Long before them, Klaua and Gottwald studied various forms of iterated fuzzy power set constructions inside classical set theory, see the references.

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Hájek, P. On arithmetic in the Cantor- Łukasiewicz fuzzy set theory. Arch. Math. Logic 44, 763–782 (2005). https://doi.org/10.1007/s00153-005-0284-0

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