Timeline for Unstable structures with unstable $\aleph_0$-categorical reducts
Current License: CC BY-SA 4.0
7 events
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| Sep 24 at 18:52 | comment | added | tomasz | @JamesEHanson: It's not clear to me either way. For a given formula $\varphi(x,y,z)$, I can certainly think of a scenario where $\varphi(x,y,z)$ allows us to have infinitely many types in the $z$ sort, but $\varphi(x,y,a)$ is $\aleph_0$-categorical for a suitably chosen $a$. But perhaps an altogether different formula without parameters would work... | |
| Sep 24 at 16:29 | comment | added | James E Hanson | Do we have any idea whether it's necessary to consider reducts with parameters? Both stability and $\aleph_0$-categoricity are invariant under adding (finitely many) parameters (i.e., $T$ satisfies one of these conditions iff $T_{\bar{a}}$ satisfies it as well). | |
| Sep 24 at 12:34 | comment | added | tomasz | @AlexKruckman: You're probably right. I guess this should not be too hard to show via o-minimality. | |
| Sep 24 at 3:58 | history | edited | Alex Kruckman |
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| Sep 23 at 23:43 | comment | added | Alex Kruckman | I doubt that any infinite discrete linear order has an unstable $\aleph_0$-categorical reduct. | |
| Sep 23 at 19:21 | history | edited | James E Hanson | CC BY-SA 4.0 |
Typo in title
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| Sep 23 at 19:05 | history | asked | tomasz | CC BY-SA 4.0 |