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  • 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).
  • 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). (en)
Title
  • On Equality and Natural Numbers in Cantor-Lukasiewicz Set Theory
  • On Equality and Natural Numbers in Cantor-Lukasiewicz Set Theory (en)
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  • On Equality and Natural Numbers in Cantor-Lukasiewicz Set Theory
  • On Equality and Natural Numbers in Cantor-Lukasiewicz Set Theory (en)
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  • RIV/67985807:_____/13:00343863!RIV13-AV0-67985807
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  • 1
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  • RIV/67985807:_____/13:00343863
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  • Lukasiewicz logic; Cantor set theory; full comprehension (en)
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  • GB - Spojené království Velké Británie a Severního Irska
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  • [1D028BAA634B]
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  • Logic Journal of the IGPL
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  • 21
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  • Hájek, Petr
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  • 000313837700008
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  • 1367-0751
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  • 10.1093/jigpal/jzq019
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