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Results tagged with set-theory
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user 7154
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.
38
votes
5
answers
9k
views
Completion of ZFC
I attended a talk given by W. Hugh Woodin regarding the Ultimate L axiom and I wanted to verify my current understanding of what the search for this axiom means. I find it to be a fascinating topic bu …
- 1,035
14
votes
1
answer
865
views
Set theoretical realizations of the hidden variables program in quantum mechanics
The hidden variables program in quantum mechanics has been largely discredited by two powerful theorems, namely those of Bell and Kochen/Specker. Nonetheless, this program retains a certain philosophi …
- 1,035
20
votes
2
answers
4k
views
Logically independent but true sentences
My question is of a logical nature and concerns what I perceive to be two different types of mathematical independence.
Suppose we have a (sufficiently strong) axiomatic theory $T$. Gödel's Incomplet …
- 1,035
8
votes
3
answers
2k
views
Surreal Numbers and Set Theory
Hello,
I looked through MathOverflow's existing entries but couldn't find a satisfactory answer to the following question:
What is the relationship between No, Conway's class of surreal numbers, and …
- 1,035
4
votes
(Non?)-linearity of the consistency strength ordering in ZF
My understanding is that the large cardinals are indeed linearly ordered, which is a remarkable fact. Of course, it is not a theorem (nor could it ever be?), but merely an empirical fact; still, there …
- 1,035