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Some Remarks on Cantor-Lukasiewicz Fuzzy Set Theory

SYSNO ASEP	0350422
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	Some Remarks on Cantor-Lukasiewicz Fuzzy Set Theory
Author(s)	Hájek, Petr (UIVT-O)_{RID, SAI}
Source Title	Logic Journal of the IGPL. - : Oxford University Press - ISSN 1367-0751 Roč. 21, č. 2 (2013), s. 183-186
Number of pages	4 s.
Language	eng - English
Country	GB - United Kingdom
Keywords	naive comprehension scheme ; fuzzy set theory ; consistency ; Lukasiewicz logic
Subject RIV	BA - General Mathematics
R&D Projects	GAP202/10/1826 GA ČR - Czech Science Foundation (CSF)
CEZ	AV0Z10300504 - UIVT-O (2005-2011)
UT WOS	000316295100003
EID SCOPUS	84875249715
DOI	10.1093/jigpal/jzs014
Annotation	Lukasiewicz predicate logic with its standard and its general semantics is denoted by Ł. Over this logic, we study the set theory CŁ0 with full comprehension (but without extensionality; adding it would trivialize the theory, as proved by Grishin). A proof of consistency of CŁ0 was published by White, but his proof was criticized as having a gap. Here Section 1 analyses the problem of consistency of CŁ0. In Section 2, I discuss the problem of omega-inconsistency of the CŁ0 (with its general semantics) using ideas of Yatabe. Section 3 presents some construction of crisp sets in this theory.
Workplace	Institute of Computer Science
Contact	Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800
Year of Publishing	2014

Number of the records: 1