Timeline for Axiom of Countable Choice and meager sets
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Sep 13, 2020 at 20:06 | comment | added | Asaf Karagila♦ | @Andreas: That's a good point. If $\Bbb R$ can be well-ordered, but some strange sets exist above it, it would be a counterexample. I suppose that the right question, then, is restricting these choice principles to sets of reals. | |
| Sep 13, 2020 at 14:24 | history | became hot network question | |||
| Sep 13, 2020 at 13:42 | answer | added | Martin Väth | timeline score: 1 | |
| Sep 13, 2020 at 12:41 | comment | added | Andreas Blass | Since (UMM) is only about Polish spaces, it should be preserved from the ground model to symmetric extensions that introduce no new sets of low rank. So I'd be inclined to try violating (UCC) among sets of very high rank and thus answer Problem 2 negatively. | |
| Sep 13, 2020 at 8:48 | comment | added | Asaf Karagila♦ | @bof: I can't say if the answer is positive or not, but at least in Truss' model, the countable union of countable sets of reals is countable, but $\omega_1$ is singular. | |
| Sep 13, 2020 at 8:39 | history | edited | YCor |
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| Sep 13, 2020 at 7:26 | comment | added | bof | And what about (UCM), the union of a countable family of countable sets is meager? Does (UCM) imply (UCC)? | |
| Sep 13, 2020 at 7:01 | comment | added | Asaf Karagila♦ | Good questions. | |
| Sep 13, 2020 at 6:57 | history | edited | Taras Banakh | CC BY-SA 4.0 |
Added some new info.
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| Sep 13, 2020 at 6:24 | history | asked | Taras Banakh | CC BY-SA 4.0 |