Timeline for What's the use of countable ordinals? (prompted by a remark of Tim Gowers)
Current License: CC BY-SA 4.0
5 events
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| Apr 14, 2020 at 3:03 | comment | added | Yemon Choi | The reason I ask is that the outlines of the proof that I can find online do not mention ordinals: math.stackexchange.com/questions/1855549/… and mathoverflow.net/questions/47747/… Could you at least comment on which parts of those outlines are where the ordinals are hidden? | |
| Apr 13, 2020 at 21:49 | comment | added | Sov | Well, the proof is quite long ... and difficult. I do not have any better advice for you to have a look in the book (volume 2, section 1.14). The section starts with some lemmas, where we understand that a "suitable" category $\mathcal{D}$ will help us later. In the proof of the theorem, he constructs this category $\mathcal{D}$. In order to do this, a sequence of posets indexed by the ordinals is needed. (and at some point a transfinite induction is done) | |
| Apr 9, 2020 at 21:15 | comment | added | Yemon Choi | Could you please give some details of how transfinite induction is used in the proof that you are thinking of? | |
| Apr 6, 2020 at 4:18 | comment | added | Yemon Choi | So this is the Freyd-Mitchell embedding theorem, right? I don't recall any transfinite induction in the proof, but I admit it has been a long time since I sem-learned this... | |
| Apr 5, 2020 at 23:41 | history | answered | Sov | CC BY-SA 4.0 |