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Results tagged with set-theory
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user 4903
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.
1
vote
1
answer
723
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Choice function on the countable subsets of the reals
It is easy to find a choice function on all finite subsets of $\mathbb R$, but without using the axiom of choice, not on all subsets. Is there an "explicit" choice function on the countable subsets of …
- 656
12
votes
4
answers
1k
views
Universal order type
Every countable order type, such as the countable ordinals, $\mathbb Z$, etc. can be embedded in $\mathbb Q$, so it is universal for countable order types. Is there a universal space for all linear or …
- 656
2
votes
1
answer
1k
views
Total order on the powerset
Given a well ordering of a set $A$ we can define a total order $A^A$ in an obvious way (for $f \neq g$ find the least $i$ such that $f(i) \neq g(i)$ and define $f < g$ if $f(i) < g(i)$)
Does the inve …
- 656
10
votes
2
answers
911
views
Set theoretic question about real valued functions
It's a question I've been thinking about but I can't find an easy answer. I think it will be interesting. Can there be a countable collection of real valued functions $f_1, f_2 , ... $ such that for a …
- 656