Timeline for Elementary embeddings and replacement
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| May 15, 2021 at 4:49 | comment | added | Sam Roberts | Exactly! And it makes obtaining the relevant limit trivial. | |
| May 15, 2021 at 0:19 | comment | added | Gabe Goldberg | Yes, that works. And after all the theory "ZFC + infinitely many supercompacts" is not really much stronger than "ZFC + the existence of an ordinal $\alpha$ that is a limit of $\alpha$-Magidor supercompacts," which already implies the consistency of Zermelo set theory + infinitely many supercompacts. | |
| May 14, 2021 at 7:07 | vote | accept | Sam Roberts | ||
| May 14, 2021 at 7:06 | comment | added | Sam Roberts | Thanks, Gabe! That's just what I was looking for. I take it the easiest way to implement your idea is to let $\alpha$ be the limit of the first $\omega$ supercompacts. Then we get that $\beta$ is supercompact in $V_\alpha$ just in case it is supercompact simpliciter and thus that they are the first $\omega$ supercompacts from the perpsective of $V_\alpha$. | |
| May 13, 2021 at 21:09 | history | edited | Gabe Goldberg | CC BY-SA 4.0 |
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| May 13, 2021 at 14:32 | history | edited | Gabe Goldberg | CC BY-SA 4.0 |
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| May 13, 2021 at 13:36 | history | edited | Gabe Goldberg | CC BY-SA 4.0 |
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| May 13, 2021 at 13:29 | history | answered | Gabe Goldberg | CC BY-SA 4.0 |