Some Remarks on Cantor-Lukasiewicz Fuzzy Set Theory

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F13%3A00350422" target="_blank" >RIV/67985807:_____/13:00350422 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1093/jigpal/jzs014" target="_blank" >http://dx.doi.org/10.1093/jigpal/jzs014</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1093/jigpal/jzs014" target="_blank" >10.1093/jigpal/jzs014</a>

Result language
angličtina
Original language name
Some Remarks on Cantor-Lukasiewicz Fuzzy Set Theory
Original language description
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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GAP202%2F10%2F1826" target="_blank" >GAP202/10/1826: Mathematical Fuzzy Logic in Computer Science</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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