Timeline for ZF + "every Suslin set of reals is ${\bf \Sigma}^1_2$"
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Jun 19, 2018 at 23:52 | comment | added | Trevor Wilson | @Asaf Do you mean that ZF + ($\ast$) implies $\aleph_1^V$ is strong limit in $L$? I don't even see why it would imply that $\aleph_1^L < \aleph_1$. In light of the result of Martin and Solovay I mentioned, we would need to do something with $\kappa$-Suslin sets for some $\kappa > \aleph_1$, but I don't know what. | |
| Jun 19, 2018 at 21:59 | comment | added | Asaf Karagila♦ | Well. If $\omega_1$ is regular, the lower bound would be at least an inaccessible, almost automatically. My guess you can get probably get something like some large cardinal using some absoluteness. | |
| Jun 19, 2018 at 15:32 | history | edited | Trevor Wilson | CC BY-SA 4.0 |
typo
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| Jun 19, 2018 at 15:31 | comment | added | Trevor Wilson | @Asaf I would be interested in the answer either way (as written, or with DC). The equiconsistency that I mentioned holds with or without DC added. The model of ($\ast$) + "$\Theta = \aleph_2$" that I obtain from a model of ZFC + "there is a generic Vopěnka cardinal" satisfies DC, but the reverse direction does not require any kind of choice principle. | |
| Jun 19, 2018 at 7:14 | comment | added | Asaf Karagila♦ | I am guessing that you also want DC there, or at least DC(R), right? | |
| Jun 17, 2018 at 0:32 | history | asked | Trevor Wilson | CC BY-SA 4.0 |