Timeline for How this set of functions is ordered?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2023 at 15:48 | comment | converted from answer | Andreas Weiermann | I think being able to prove that a lower bound for the resulting order type is given by $\varphi\omega0$. It is not clear whether one can reach $\Gamma_0$ at the end. | |
| Apr 6, 2023 at 15:22 | comment | converted from answer | Andreas Weiermann | I think that the suggested problem is very interesting. My guess would be that the resulting order type (after Harry's modification) should be about $\Gamma_0$. | |
| Mar 15, 2023 at 14:37 | answer | added | Harry Altman | timeline score: 1 | |
| Dec 31, 2011 at 21:52 | vote | accept | Vladimir Reshetnikov | ||
| Dec 7, 2011 at 21:18 | comment | added | Harry Altman | Yikes -- not certain my proof of the above comment is correct, or that the comment is correct. Same applies where I stated the same in my answer below, of course. Of course, since I've since solved the problem (as stated), it's kind of irrelevant... | |
| Dec 4, 2011 at 0:51 | comment | added | Harry Altman | Hm... the obvious way to contradict well-ordering would be to construct the predecessor function, but this is impossible; for any $f\in S$, $\mathbb{N}$ can be split into two sets A and B such that f is bounded on A and satisfies $f(n)\ge n$ on B. (Omitting proof because once you think to make the statement, it's straightforward.) | |
| Dec 3, 2011 at 23:49 | comment | added | Joel David Hamkins | Harry, I would think that for a lower bound of $\alpha$ Vladimir would simply want us to exhibit a collection of functions having order type $\alpha$ under eventual domination. And the bigger the $\alpha$, the more nontrivial the bound. | |
| Dec 3, 2011 at 22:18 | answer | added | Harry Altman | timeline score: 7 | |
| Dec 3, 2011 at 21:26 | comment | added | Harry Altman | I think it's obvious what would count as a nontrivial upper bound, but what counts as a nontrivial lower bound? | |
| Dec 3, 2011 at 20:35 | history | edited | Vladimir Reshetnikov | CC BY-SA 3.0 |
added 85 characters in body
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| Dec 1, 2011 at 19:06 | history | asked | Vladimir Reshetnikov | CC BY-SA 3.0 |