Jul
2
awarded Curious
Apr
8
accepted A couple questions about a countable set I encountered
Apr
8
comment A couple questions about a countable set I encountered
Thanks for the reply. It definitely makes more sense when you picture $f$ and $g$ as sequences.
Apr
7
comment A couple questions about a countable set I encountered
@AndresCaicedo From what I remember, the set of all finite subsets of $\omega$ is countable.
Apr
7
asked A couple questions about a countable set I encountered
Jan
29
awarded Popular Question
Nov
20
awarded Yearling
Nov
20
awarded Yearling
Oct
29
accepted Relative Consistency proof for the Axiom of Choice
Oct
29
comment Relative Consistency proof for the Axiom of Choice
Thanks again Asaf! This was, yet again, one of those problems where I thought about it too much and made it more difficult than it really is.
Oct
29
comment Relative Consistency proof for the Axiom of Choice
From your hint, since $\bigcup F \subseteq \mbox{trcl}(F)$, $\bigcup F$ is well-ordered since any subset of a well-ordered set is well-ordered. Wouldn't it follow that we can find a choice function since $\bigcup F$ is well-ordered?
Oct
29
revised Relative Consistency proof for the Axiom of Choice
fixed my wording
Oct
29
comment Relative Consistency proof for the Axiom of Choice
@AndresCaicedo I might have. Sorry about that. I will fix my wording.
Oct
29
asked Relative Consistency proof for the Axiom of Choice
Oct
28
accepted Transitive closure of a union
Oct
28
comment Transitive closure of a union
Thanks for the helpful hint! I was able to show equality.
Oct
28
revised Transitive closure of a union
added 48 characters in body
Oct
28
asked Transitive closure of a union
Oct
21
comment Showing that intersections are not defined
Interesting. Thanks again for your help.
Oct
21
accepted Showing that intersections are not defined
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