Timeline for Models of ZFC and the Borel hierarchy
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 14, 2017 at 6:53 | vote | accept | Bjørn Kjos-Hanssen | ||
| Aug 18, 2017 at 0:17 | vote | accept | Bjørn Kjos-Hanssen | ||
| Aug 18, 2017 at 15:45 | |||||
| Aug 18, 2017 at 0:17 | answer | added | Bjørn Kjos-Hanssen | timeline score: 1 | |
| Apr 14, 2017 at 20:09 | comment | added | Samuel Coskey | My student Samuel Dworetzky showed that the isomorphism relation for countable models of ZFC is Borel complete (in the sense of Borel complexity theory). I don't think it affects this particular question, though. | |
| Apr 11, 2017 at 21:36 | history | edited | Bjørn Kjos-Hanssen | CC BY-SA 3.0 |
forgot to mention con(ZFC)
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| Apr 11, 2017 at 21:22 | comment | added | Joel David Hamkins | @FrançoisG.Dorais Why not expand your comment to an answer? | |
| Apr 11, 2017 at 20:52 | comment | added | François G. Dorais | By reading the axioms (i.e. every axiom is satisfied, as a formalized statement) it's a $\Pi^0_{\omega+1}$ set (since satisfying a first-order sentence is $\Pi^0_n$ for some $n$). I think that it's not $\Pi^0_n$ for $n<\omega$ amounts to the fact that ZFC is not finitely axiomatizable. | |
| Apr 11, 2017 at 19:18 | comment | added | Joel David Hamkins | I think that Sam Coskey was looking at the isomorphism relation on these models under Borel reducibility, aiming to place it in the hierarchy of Borel reducibility. | |
| Apr 11, 2017 at 19:14 | history | edited | Bjørn Kjos-Hanssen | CC BY-SA 3.0 |
added 59 characters in body
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| Apr 8, 2017 at 16:46 | comment | added | Andreas Blass | "Complete for level $\omega$" looks plausible. | |
| Apr 8, 2017 at 14:23 | comment | added | Andreas Blass | Usually, "complete for X" means (1) in X and (2) at least as complicated as anything else in X. Presumably, by "in some sense complete for finite levels of the Borel hierarchy", you meant only (2). | |
| Apr 8, 2017 at 7:29 | history | asked | Bjørn Kjos-Hanssen | CC BY-SA 3.0 |