Počet záznamů: 1

Some Remarks on Cantor-Lukasiewicz Fuzzy Set Theory

  1. 1.
    0350422 - UIVT-O 2014 RIV GB eng J - Článek v odborném periodiku
    Hájek, Petr
    Some Remarks on Cantor-Lukasiewicz Fuzzy Set Theory.
    Logic Journal of the IGPL. Roč. 21, č. 2 (2013), s. 183-186 ISSN 1367-0751
    Grant CEP: GA ČR GAP202/10/1826
    Výzkumný záměr: CEZ:AV0Z10300504
    Klíčová slova: naive comprehension scheme * fuzzy set theory * consistency * Lukasiewicz logic
    Kód oboru RIV: BA - Obecná matematika
    Impakt faktor: 0.530, rok: 2013

    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.
    Trvalý link: http://hdl.handle.net/11104/0190435