Timeline for Strictly descending sequences of sets, the Partition Principle, and the Boolean Prime Ideal Theorem
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Jul 14, 2021 at 18:33 | history | edited | Asaf Karagila♦ |
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| Jul 14, 2021 at 15:50 | vote | accept | Dominic van der Zypen | ||
| Jul 14, 2021 at 12:07 | comment | added | Asaf Karagila♦ | @Sam: I said almost. In every place it is mentioned, it is also mentioned that we know practically nothing about it, except the obvious implications. So this is the choice principle equivalent of asking what is dark matter. | |
| Jul 14, 2021 at 12:01 | comment | added | Sam Hopkins | @AsafKaragila: I don't think it's fair to call a question "disingenuous," at least not without strong evidence of the asker's motivations. | |
| Jul 14, 2021 at 11:51 | answer | added | Asaf Karagila♦ | timeline score: 6 | |
| Jul 14, 2021 at 11:19 | comment | added | Asaf Karagila♦ | Asking questions about PP is almost disingenuous. We don't know of any models of ZF where it holds and choice fails. | |
| Jul 14, 2021 at 11:18 | comment | added | Asaf Karagila♦ | Throwing a stone into a well is a lot easier than digging it out. | |
| Jul 14, 2021 at 9:29 | comment | added | Joel David Hamkins | I would find it more natural, in both of your questions, to consider whether the cardinals are well-founded, that is, whether every set of sets has a member of minimal cardinality. This prevents a descending $\omega$-sequence, but without AC (specifically, without DC), the failure of well-foundedness doesn't seem to imply that there must be a descending $\omega$-sequence, since you'd have to pick the sets. So well-foundedness appears to be stronger than the nonexistence of a descending $\omega$-sequence. | |
| Jul 14, 2021 at 8:46 | comment | added | Wojowu | Related | |
| Jul 14, 2021 at 8:16 | history | asked | Dominic van der Zypen | CC BY-SA 4.0 |