Timeline for Absoluteness of well-orderability
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Jul 14, 2023 at 16:28 | comment | added | Julia Williams | @AdamEpstein My argument assumed a model of ZFC whose well-founded part contains an admissible ordinal $>\omega$, which is epsilon below having a transitive model. But that was just for convenience. It only takes a finite fragment of ZFC to prove that $V_{\omega+\omega}$ satisfies Z. You can run the same argument with a model $\bar M$ of KP + that finite fragment, and that's good enough to conclude that well-foundedness is not upward absolute for transitive models of Z. And of course ZFC proves the consistence of KP + that finite fragment, so we don't need to go beyond ZFC in consistency. | |
| Jul 12, 2023 at 8:09 | comment | added | Adam Epstein | Is the Friedman Lemma being applied to ZFC? Wouldn't this mean you are assuming the existence of a transitive model of ZFC? | |
| Jul 12, 2023 at 8:03 | vote | accept | Adam Epstein | ||
| Oct 19, 2022 at 14:54 | history | answered | Julia Williams | CC BY-SA 4.0 |