Timeline for Strongest large cardinal axiom compatible with $V = L$?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Oct 23, 2022 at 22:42 | vote | accept | Jesse Elliott | ||
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Dec 13, 2014 at 15:53 | comment | added | Yair Hayut | Another way to cheat and get slightly stronger large cardinals: it is consistent that there is an ordinal $\alpha$, $V=L$ and in some generic extension (by a set forcing notion) there is an $\alpha$-Erdos cardinal, even when $\alpha$ is not countable in $L$. | |
| Dec 13, 2014 at 4:29 | answer | added | Mohammad Golshani | timeline score: 13 | |
| Dec 13, 2014 at 1:23 | comment | added | Andrés E. Caicedo | Your suggestion is essentially it. The modern presentation of $0^\sharp$ is as what Schimmerling calls a baby mouse, this is a structure $J_\tau$ with an external measure that is iterable (and some technical definability requirements). Asking that for each $\alpha<\omega_1$ there is such a structure, but only $\alpha$-iterable, seems as strong as possible. But this is in essence the same as considering $\alpha$-Erdős cardinals. | |
| Dec 13, 2014 at 1:12 | history | asked | Jesse Elliott | CC BY-SA 3.0 |