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Results tagged with set-theory
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user 4137
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.
12
votes
Completion of ZFC
Alex, you ask a lot of questions, and I'm in no position to say much about Ultimate L. I'll just address this initial matter:
And how do we know that there are (infinitely) many different completion …
- 2,305
5
votes
Independence of P = NP?
This answer started life as a nascent comment intended for the back-and-forth above, but it ballooned into what follows.
ZW, as I pointed out above, your current question does parallel your earlier qu …
- 2,305
10
votes
Axiomatic Set Theory
Foundations of Set Theory by Fraenkel, Bar-Hillel and Levy is a classic that provides what it sounds like you're after. It surveys ZF and its milieu, type-theoretic approaches (including Quine's New F …
11
votes
A question about Quine's set theory NF.
One can give stratified definitions for individual Frege-Russell natural numbers, and then so too for the set $\mathbb{N}$ of all Frege-Russell naturals, so that exists in NF. One can then check that …
- 2,305
1
vote
Limiting set theory using symmetry
If you're sure the paper in mind was on the arxiv, then this paper of Harvey Friedman's isn't it. But since you're after "corroboration for a line of thought [you are] pursuing at the moment," maybe …
- 2,305
13
votes
How much of ZFC does Quine's New Foundations prove?
NF does prove Cantor's theorem in the sense you indicate, $|\mathscr{P}_1(X)|<|\mathscr{P}(X)|$ for any set $X$. The usual ZF proof goes through, because definitions in that proof which need to be st …
- 2,305
6
votes
What did Zermelo say he was hoping for on the consistency of set theory?
The following remarks may not speak to what you're really after, but given your explicit reference to Hilbert's Program still being years away when wondering what Zermelo might have in mind, they may …
- 2,305
19
votes
Essential reads in the philosophy of mathematics and set theory
Benacerraf and Putnam's Philosophy of Mathematics: Selected Readings is a pretty standard (as these things go) collection of seminal papers in the philosophy of mathematics generally, and in the philo …