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Aug
22
comment A question about cardinal numbers when the Axiom of Choice is absent
Many thanks, Asaf, for your response. I am amazed because I was sure the answer would be "No".
Aug
21
asked A question about cardinal numbers when the Axiom of Choice is absent
Aug
17
comment A question about ordinal numbers and sub-theories of ZF
Thanks for the information
Aug
15
comment Two questions about convex subsets of Hilbert Space
Many thanks, Christian, for this information.
Aug
15
accepted Two questions about convex subsets of Hilbert Space
Aug
15
asked Two questions about convex subsets of Hilbert Space
Aug
15
comment A question about ordinal numbers and sub-theories of ZF
What does "close (2)" mean? Is this question closed out? It is a rather "fuzzy" question and I can understand why some would vote to close it. Prior to asking this question, I had asked 99 questions on "mathoverflow.net". Why is the total number of my questions still listed as 99-instead of a larger number.
Aug
14
comment A question about ordinal numbers and sub-theories of ZF
Andreas, you are right. But what I am asking is, which of the axioms of ZF are actually needed to prove the existence of a all the sets which satisfy von Neumann's formula defining wjch sets are ordinal numbers and which belong to the set theoretic hierarchy of ZF.
Aug
13
comment A question about ordinal numbers and sub-theories of ZF
@Andreas: Levy showed that there existed no formula A(x) in the language of ZF, containing x as its one and only free variable, which expressed the statement "x is a Cardinal Number". Ordinal numbers are defined by such formulae in ZF and it is then proved in ZF that sets satisfying these definitions exist. I am asking whether all the axioms of ZF are needed to carry out these proofs.
Aug
12
asked A question about ordinal numbers and sub-theories of ZF
Jul
28
awarded  Popular Question
Jul
8
comment One or two questions about so-called “absolute” set theories
"Absolute" set theory (or theories) are defined and discussed on pages 79-80 of the book "Foundations of Mathematics: Symposium Papers Commemorating the Sixtieth Birthday of Kurt Godel" which was published in 1969 by Springer Verlag. The article by Takeuti entitled "The Universe of Set Theory" appears on pages 74-128 of this book. After defining "absolute" set theories, Takeuti does not say much more about them in this article. That is why I am asking whether there has been any further work in tis area.
Jul
6
comment Can a “weak” topological space be a Moore space?
@Christian Remling: Many thanks for your response. Since the space l^2 is separable, it seems that if we take B to be l^2, then the anmswer to my question is "YES".
Jul
6
asked One or two questions about so-called “absolute” set theories
Jul
6
awarded  Notable Question
Jul
5
comment Can a “weak” topological space be a Moore space?
A Moore space is a regular, Hausdorff developable topological space
Jul
4
asked Can a “weak” topological space be a Moore space?
Jul
2
awarded  Inquisitive
Jul
2
awarded  Curious
Jun
16
comment A question about “local” versus “global” large cardinal axioms
@ Joel: Many thanks for your answer. It seems then that the least cardinal satisfying any global property can never be less than the least cardinal satisfying any local property.