Timeline for Without choice, can every homomorphism from a profinite group to a finite group be continuous?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 10, 2022 at 21:30 | history | bounty ended | David E Speyer | ||
| Feb 9, 2022 at 13:53 | comment | added | David E Speyer | Okay, I found a way to fix this issue, and wrote it up here. mathoverflow.net/questions/290491 | |
| Feb 9, 2022 at 1:17 | comment | added | David E Speyer | Given choice, I know how to proceed: The union of countably many countable sets is countable, but $\omega_1$ isn't, QED. But without choice, the union of countably many countable sets doesn't have to be countable, so I am missing a step (probably a very small one). | |
| Feb 9, 2022 at 1:16 | comment | added | David E Speyer | Thanks! I am missing one detail in the $V \to V^{\ast \ast}$ section. I am trying to understand how we know that $\beta$ is not $\omega_1$. In other words, I want to know that a set which has finite intersection with any initial segment of $\omega_1$ is finite. I think the intended method is to show that any countable subset of $\omega_1$ has an upper bound within $\omega_1$ or, to put it another way, I want to know that $\omega_1$ is not the union of countably many proper initial segments. | |
| Feb 7, 2022 at 23:57 | comment | added | Timothy Chow | @HarryWest It seems that you have (inadvertently) answered another MO question that currently has a bounty on it. Perhaps you could post an answer to that question as well? | |
| Aug 9, 2021 at 20:11 | comment | added | Asaf Karagila♦ | Huh. You're absolutely right. Now I'm curious as to how I got my copy. I guess I asked Andreas? | |
| Aug 9, 2021 at 19:51 | comment | added | Harry West | @AsafKaragila: I tripled checked math.lsa.umich.edu/~ablass/set.html and still don't see it. (It might be nice to see, but my own curiosity was sated by filling in the details of your sketch and the summary in Pincus-Solovay.) | |
| Aug 7, 2021 at 15:06 | comment | added | Asaf Karagila♦ | Andreas' paper is available on his homepage. It's short and it's very nice. | |
| Aug 7, 2021 at 11:45 | history | edited | Gro-Tsen | CC BY-SA 4.0 |
missing negation
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| Aug 7, 2021 at 11:31 | history | answered | Harry West | CC BY-SA 4.0 |