Počet záznamů: 1

On Equality and Natural Numbers in Cantor-Lukasiewicz Set Theory

  1. 1.
    0343863 - UIVT-O 2013 RIV GB eng J - Článek v odborném periodiku
    Hájek, Petr
    On Equality and Natural Numbers in Cantor-Lukasiewicz Set Theory.
    Logic Journal of the IGPL. Roč. 21, č. 1 (2013), s. 91-100 ISSN 1367-0751
    Grant CEP: GA MŠk(CZ) 1M0545
    Výzkumný záměr: CEZ:AV0Z10300504
    Klíčová slova: Lukasiewicz logic * Cantor set theory * full comprehension
    Kód oboru RIV: BA - Obecná matematika
    Impakt faktor: 0.530, rok: 2013

    Two equality predicates in Cantor-Lukasiewicz set theory (with full comprehension, over Lukasiewicz predicate logic) are investigated: extensional =e and Leibniz equality =. It is proved that there are many pairs of sets x,y such that x =e y & x =/= y is true. In particular, x may be the set omega of natural numbers, defined together with ternary predicates for addition and multiplication. The main result says that the Cantor-Lukasiewicz set theory is essentially undecidable and essentially incomplete. The proof is difficult since it is not supposed that the set omega is crisp (non-fuzzy).
    Trvalý link: http://hdl.handle.net/11104/0186240