Timeline for Is this notion of finiteness closed under unions?
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 24, 2021 at 19:26 | vote | accept | Noah Schweber | ||
| Jun 24, 2021 at 18:39 | answer | added | Harry West | timeline score: 3 | |
| Dec 6, 2020 at 23:00 | comment | added | Noah Schweber | @JoelDavidHamkins Asaf made a nice observation at the MSE version: that we can detect, mod finite anyways, the partition of a union of finitely many amorphous sets into those original amorphous pieces. I don't immediately see how to use that here, but it might be helpful. | |
| S Nov 29, 2020 at 20:00 | history | bounty ended | CommunityBot | ||
| S Nov 29, 2020 at 20:00 | history | notice removed | CommunityBot | ||
| S Nov 21, 2020 at 18:41 | history | bounty started | Noah Schweber | ||
| S Nov 21, 2020 at 18:41 | history | notice added | Noah Schweber | Draw attention | |
| Nov 21, 2020 at 18:41 | comment | added | Noah Schweber | @JoelDavidHamkins I don't immediately see how to do that, although I could be missing something. | |
| Nov 9, 2020 at 11:00 | comment | added | Asaf Karagila♦ | Damn, I just noticed a typo in my comment. I did write it before waking up, though. "ad" $\mapsto$ "have". | |
| Nov 9, 2020 at 9:42 | comment | added | Joel David Hamkins | I think one might hope to prove that the finite union of amorphous sets is psuedo-finite, using the same model theoretic arguments that Noah mentioned. | |
| Nov 9, 2020 at 9:17 | comment | added | Asaf Karagila♦ | At least in the amorphous case it's fine. The union of two amorphous sets is amorphous or they ad a finite intersection. Does that help? | |
| Nov 9, 2020 at 9:09 | comment | added | Emil Jeřábek | No, wait, this only works if the structure on $X$ is a disjoint union of its restrictions to $A$ and $B$, not if there are nontrivial relations between elements of $A$ and $B$. | |
| Nov 9, 2020 at 8:55 | comment | added | Emil Jeřábek | (I’m assuming that the $\sqcup$ notation refers to disjoint union. Of course, since $\Pi^1_1$-pseudofiniteness is stable under subsets, this is equivalent to the general case.) | |
| Nov 9, 2020 at 8:51 | comment | added | Emil Jeřábek | It does not matter if $X$ sees the partition or not. (You could expand it with $A$ as a new predicate, if you really needed it, but you don’t.) As long as you are in a finite relational language, for any $n$, you can find finite $A'$ and $B'$ that are $n$-equivalent to the restrictions of the structure on $X$ to $A$ and $B$ respectively, and then $A'\sqcup B'$ is $n$-equivalent to $X$ by an Ehrenfeucht–Fraïssé argument. | |
| Nov 9, 2020 at 5:35 | history | asked | Noah Schweber | CC BY-SA 4.0 |