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Martin Sleziak
Martin Sleziak
10:42 AM
> I am a self-studier with no math background. I recently posted this question which received three outstanding and generously informative answers: How does the Axiom of Choice affect the ability to determine that $|\mathcal{P}(\omega)|$ is an uncountable cardinal
> The material contained in their answers, I either missed or was not presented in the context of my question in the books I have been studying.
> I would like to ask each of the responders for their suggestion(s) for study materials that might explain things as they presented them.
As far as I can tell, this seems to be mostly related to Axiom of Choice, perhaps well-orderings and ordinals. And various approaches to cardinals without ZF.
I am reposting it here in case somebody has a suggestion.
So far I have only suggested this (it is possible that the OP finds there something that is satisfactory for him):
In your deleted post on meta you've mentioned you are looking for related literature. Maybe you could have a look at posts tagged axiom-of-choice+book-recommendation (and maybe more generally set-theory+book-recommendation) to see whether some of the suggestions there is what you're looking for. — Martin Sleziak 6 hours ago
I have mentioned your question also in set theory chatroom. Although not many users visit that room, so likelihood of getting some answer there is not that high. (Feel free to visit that room if you have something related - or some of other chatrooms around here. It seems that you are also interested in logic, that room is rather active.) — Martin Sleziak 26 secs ago
 
 
3 hours later…
Feeds
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1:19 PM
1
Q: Question on a proof of Kuratwoski's Theorem in Kechris's Classical Descriptive Set Theory

IdonknowCurrently I am reading Kechris's Classical Descriptive Set Theory. Theorem $22.18$: (Kuratowski) Let $(X,\tau)$ be a Polish space and $A_n\subseteq X$ be $\Delta_\xi^0(X,\tau).$ Then there is a Polish topology $\tau'\supseteq \tau$ such that $\tau'\subseteq\Sigma_\xi^0(X,\tau)$ and $A_n\in\...

set-theory proof-explanation descriptive-set-theory borel-sets
 
 
9 hours later…
Martin Sleziak
Martin Sleziak
10:22 PM
So it seems that he is satisfied with Herrlich's book Axiom of Choice.
@MartinSleziak Dear Martin - Thank you again for your kind initiative in helping me find relevant materials. I do love math and only hope to find material that I can engage with. As it happens, thanks to you I did find what may be a promising book, Herrlich's "AoC." So far so good anyway., although sometimes accessible beginnings have a short half-life. Best regards, — Andrew 56 mins ago
 

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