Timeline for Does there always exist a categorical extension of $ZFC_2$ with no set models?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Nov 28, 2021 at 1:43 | comment | added | Elliot Glazer | $\kappa$ has the property $`` \exists \alpha < \kappa$ such that $V_{\alpha} \equiv_{\text{SOL}} V_{\kappa}"$ because $M$ thinks $j(\kappa)$ has that property. | |
| Nov 28, 2021 at 0:33 | comment | added | Noah Schweber | @ElliotGlazer Isn't that $M$-superscript a problem though? | |
| Nov 28, 2021 at 0:32 | comment | added | Elliot Glazer | Yes measurables work, because for $j: V \rightarrow M$ with critical point $\kappa,$ $V_{\kappa+1}^M$ and $V_{j(\kappa)+1}^M$ have the same theory. | |
| Nov 27, 2021 at 23:11 | comment | added | Noah Schweber | @AsafKaragila Yes, basically $\Sigma^1_\omega$-indescribability (for theories instead of individual sentences, but I don't think that changes the strength too much). I guess measurables, being $\Pi^2_1$-indescribable, would probably do the trick. | |
| Nov 27, 2021 at 22:42 | comment | added | Asaf Karagila♦ | Wouldn't that be something similar to indescribable cardinals? | |
| Nov 27, 2021 at 22:22 | history | edited | Noah Schweber | CC BY-SA 4.0 |
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| Nov 27, 2021 at 22:14 | history | answered | Noah Schweber | CC BY-SA 4.0 |