On arithmetic in the Cantor- Łukasiewicz fuzzy set theory

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

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.

Categories

Keywords

Reprint years

DOI

10.1007/s00153-005-0284-0

Other Versions

No versions found

Links

PhilArchive

    This entry is not archived by us. If you are the author and have permission from the publisher, we recommend that you archive it. Many publishers automatically grant permission to authors to archive pre-prints. By uploading a copy of your work, you will enable us to better index it, making it easier to find.

    Upload a copy of this work     Papers currently archived: 106,126

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Comprehension contradicts to the induction within Łukasiewicz predicate logic.Shunsuke Yatabe - 2009 - Archive for Mathematical Logic 48 (3-4):265-268.
Distinguishing non-standard natural numbers in a set theory within Łukasiewicz logic.Shunsuke Yatabe - 2007 - Archive for Mathematical Logic 46 (3-4):281-287.
Hájek basic fuzzy logic and Łukasiewicz infinite-valued logic.Roberto Cignoli & Antoni Torrens - 2003 - Archive for Mathematical Logic 42 (4):361-370.
On witnessed models in fuzzy logic II.Petr Hájek - 2007 - Mathematical Logic Quarterly 53 (6):610-615.
Some remarks on Cantor-Lukasiewicz fuzzy set theory.P. Hajek - 2013 - Logic Journal of the IGPL 21 (2):183-186.
Joint Consistency of Fuzzy Theories.Vilém Novák - 2002 - Mathematical Logic Quarterly 48 (4):563-573.
Mathematics Behind Fuzzy Logic.Esko Turunen - 1999 - Physica-Verlag Heidelberg.
Omitting types in fuzzy logic with evaluated syntax.Petra Murinová & Vilém Novák - 2006 - Mathematical Logic Quarterly 52 (3):259-268.
Fuzzy logic and fuzzy set theory.Gaisi Takeuti & Satoko Titani - 1992 - Archive for Mathematical Logic 32 (1):1-32.
Commutative basic algebras and non-associative fuzzy logics.Michal Botur & Radomír Halaš - 2009 - Archive for Mathematical Logic 48 (3-4):243-255.

Analytics

Added to PP
2013-10-30

Downloads
49 (#497,525)

6 months
9 (#445,453)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

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

View all 8 citations / Add more citations

References found in this work

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.

View all 13 references / Add more references