Timeline for Undetermined Banach-Mazur games: beyond DC
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Dec 7, 2020 at 11:17 | comment | added | Alessandro Codenotti | It's not quite a Banach-Mazur game, but if you're not aware of it already 21.4 in Kechris's classical DST (see also the long hint at the end of the book) asks to construct a non quasidetermined game in ZF, maybe that construction can be modified | |
| S Mar 11, 2020 at 22:01 | history | bounty ended | CommunityBot | ||
| S Mar 11, 2020 at 22:01 | history | notice removed | CommunityBot | ||
| Mar 4, 2020 at 1:14 | history | edited | Noah Schweber | CC BY-SA 4.0 |
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| Mar 3, 2020 at 21:05 | comment | added | James E Hanson | It's actually not clear to me that DC implies that any weakly determined BM game is determined. | |
| Mar 3, 2020 at 21:04 | comment | added | James E Hanson | ZF+¬DC implies that there is a BM game that fails to be weakly determined. Take a pruned tree of height $\omega$ with no paths and put the upper set topology on it. The quasistrategy of responding to any move with the cone above some element not minimal in the previous set is winning for both players. | |
| S Mar 3, 2020 at 20:17 | history | bounty started | Noah Schweber | ||
| S Mar 3, 2020 at 20:17 | history | notice added | Noah Schweber | Draw attention | |
| Mar 3, 2020 at 20:17 | history | edited | Noah Schweber | CC BY-SA 4.0 |
added 826 characters in body; edited title
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| Feb 7, 2020 at 23:30 | comment | added | Asaf Karagila♦ | If it helps, I have a model where every set is the image of a Dedekind-finite set... | |
| Feb 7, 2020 at 22:58 | comment | added | Asaf Karagila♦ | I meant the Gitik model as well. | |
| Feb 7, 2020 at 22:58 | comment | added | Noah Schweber | @AsafKaragila I meant the Gitik model. | |
| Feb 7, 2020 at 22:57 | comment | added | Asaf Karagila♦ | If it was easy you'd have solved it by now... | |
| Feb 7, 2020 at 22:57 | comment | added | Noah Schweber | @AsafKaragila Yeah, I'm looking at it but it's really complicated. | |
| Feb 7, 2020 at 22:26 | comment | added | Asaf Karagila♦ | My guess is that looking at Gitik's model would be a good starting point. | |
| Feb 7, 2020 at 20:09 | history | asked | Noah Schweber | CC BY-SA 4.0 |