Timeline for Non-rigid ultrapowers in $\mathsf{ZFC}$?
Current License: CC BY-SA 4.0
23 events
| when toggle format | what | by | license | comment | |
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| Mar 16, 2022 at 16:54 | comment | added | Noah Schweber | @PaulLarson " An ultrapower of a structure of infinite Scott height by an ultrafilter on omega shouldn't have its points separated by its Scott process. Should that make it nonrigid?" I'm not certain, I'm not too familiar with Scott processes. | |
| Mar 16, 2022 at 16:45 | comment | added | Paul Larson | The proof of Harrington's theorem on the Scott ranks of counterexamples to Vaught's Conjecture should show that separating points characterizes rigidity for structures of size aleph_1 too. | |
| Mar 16, 2022 at 15:34 | comment | added | Paul Larson | A countable structure is rigid if and only if its Scott process separates points. An ultrapower of a structure of infinite Scott height by an ultrafilter on omega shouldn't have its points separated by its Scott process. Should that make it nonrigid? | |
| Mar 16, 2022 at 15:11 | comment | added | Noah Schweber | @PaulLarson Ooh, fun question (although not directly related to this one unless I'm missing something?) - I can't think of anything off the top of my head, but this is well outside my normal sphere so that doesn't mean much. | |
| Mar 16, 2022 at 14:57 | comment | added | Paul Larson | Is there anything known about rigid structures whose countable elementary substructures are all non-rigid? | |
| S Feb 10, 2022 at 20:07 | history | bounty ended | CommunityBot | ||
| S Feb 10, 2022 at 20:07 | history | notice removed | CommunityBot | ||
| S Feb 2, 2022 at 18:41 | history | bounty started | Noah Schweber | ||
| S Feb 2, 2022 at 18:41 | history | notice added | Noah Schweber | Draw attention | |
| S Jan 10, 2022 at 21:06 | history | bounty ended | CommunityBot | ||
| S Jan 10, 2022 at 21:06 | history | notice removed | CommunityBot | ||
| Jan 3, 2022 at 16:57 | comment | added | Noah Schweber | @FarmerS Good question! :P The best I can say is that Shelah's Vive la difference series probably has some relevant info, per Douglas Ulrich's comment, but I haven't worked through those papers to see if there's an answer there. | |
| Jan 3, 2022 at 13:00 | comment | added | Farmer S | Maybe this is easy, but do we know there is a countably infinite structure and some non-principal ultrafilter on $\omega$ such that the ultraproduct is rigid? | |
| S Jan 2, 2022 at 19:37 | history | bounty started | Noah Schweber | ||
| S Jan 2, 2022 at 19:37 | history | notice added | Noah Schweber | Draw attention | |
| S Nov 20, 2021 at 20:03 | history | bounty ended | CommunityBot | ||
| S Nov 20, 2021 at 20:03 | history | notice removed | CommunityBot | ||
| Nov 15, 2021 at 16:53 | history | edited | Noah Schweber |
edited tags
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| S Nov 12, 2021 at 18:24 | history | bounty started | Noah Schweber | ||
| S Nov 12, 2021 at 18:24 | history | notice added | Noah Schweber | Draw attention | |
| Nov 10, 2021 at 16:49 | history | edited | Noah Schweber | CC BY-SA 4.0 |
added 98 characters in body
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| Nov 10, 2021 at 16:07 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
a minor typo
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| Nov 10, 2021 at 16:01 | history | asked | Noah Schweber | CC BY-SA 4.0 |