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Results tagged with set-theory
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user 158
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
5
answers
1k
views
Questions about ordering of reals and irrationals
Three problems from G.Rosenstein "Linear orderings" (from the end of Chapter 2 and beginning of Chapter 4):
1) Is there a nondecreasing function from irrationals onto reals?
2) Is there a nondecreas …
- 918
13
votes
2
answers
2k
views
Ordinals that are not sets
The class of all ordinal numbers $\mathbf{Ord}$, aside being a proper class, can be thought of an ordinal number (of course it contains all ordinal numbers that are sets, not itself). Then one could c …
- 918
7
votes
4
answers
964
views
Higher-rank Borel sets
What are interesting, illustrative examples of Borel sets, situated in Borel hierarchy higher than $\Sigma^{0}_{2}$ /$\Pi^{0}_{2}$?
- 918