NF consistency proof via construction of parent functions
نویسنده
چکیده
parent function, definition be-gins, 26abstract parent function, definition com-pleted, 30allowable permutation, 28ambiguity, axiom scheme of, 13anomaly of a near litter, 34atom, irregular, 27atoms, regular, 26axiom of weak extensionality, 15axiom scheme of ambiguity, 13axioms of NF, 11axioms of TST, 8, 10 Choice false in NF, 13Choice, axiom of, 9clan, 26clan index, 27coding function, defined, 34coding function, restricted, 37complexity condition on abstract par-ent sets, 29complexity of an object, 29comprehension in NF, 11comprehension in TST, 8comprehension in TSTλ, 10comprehension, stratifiied, axiom of,12consistency of NFU, 16 double power set lemma, 41downward extension relation on ex-tended type indices, defined,25 elementarity property of tangled webs,23Erdös-Rado theorem, 20exception (of an allowable permuta-tion), 30extended type index, 23extended type index, defined, 25extension property for nice functions/maps,33extensionality in NF, 11extensionality in TST, 8extensionality in TSTλ, 10 Frankel-Mostowski construction, 38 hereditarily symmetric, 28 index, clan, 27index, extended type, 25index, type, 25Infinity a theorem of NF, 13Infinity, axiom of, 9 large set, defined, 25litter, 26local cardinal, 26locally small bijection, 30
منابع مشابه
Clans, parent sets, litters, atoms, and allowable permutations
Introductory remarks: In this note I am trying to separate out another theme in my NF consistency proof, namely the basic maneuver behind the FM construction. The advantage of this approach is that it makes it clear that the properties of the system of atoms, clans and litters constructed depend to very different degrees on the insane definition of the parent sets, which in this approach is int...
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