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Results tagged with set-theory
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user 33663
forcing, large cardinals, descriptive set theory, infinite combinatorics, cardinal characteristics, forcing axioms, ultrapowers, measures, reflection, pcf theory, models of set theory, axioms of set theory, independence, axiom of choice, continuum hypothesis, determinacy, Borel equivalence relations, Boolean-valued models, embeddings, orders, relations, transfinite recursion, set theory as a foundation of mathematics, the philosophy of set theory.
11
votes
Understanding Specker's disproof of the axiom of choice in New Foundations
``Work in NF, and assume the axiom of choice. Then we can prove that in general, the cardinality of a set A has greater or equal cardinality than the set of singletons drawn from A.''
I doubt this ve …
- 601
9
votes
Understanding Specker's disproof of the axiom of choice in New Foundations
Beware! Even in versions of NF that allow choice (one thinks of NFU) it is not the case that every wellordering is iso to an initial segment of the ordinals, and certainly not to a von Neumann ordinal …
- 601
14
votes
Can we have A={A} ?
Yes, these things are called Quine atoms, tho' i think there is a literature about them that goes back earlier than Quine. Yes, Forti-Honsell's antifoundation axiom (written about and popularised by …
- 601
19
votes
How much of ZFC does Quine's New Foundations prove?
One twist one can give to the question is to reformulate it as: which axioms of ZF(C) does NF prove to hold in the wellfounded sets?
We know the following: extensionality, pairing, sumset, power set, …
- 601
7
votes
Constructible models of New Foundations?
You can't do it for NF, but there is a good notion of constructible model of the theory CUS of Church, that has a universal set. But that's really just a trick of the light, since the big sets of CU …
- 601