Timeline for Critical points of rank-into-rank embeddings
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Nov 14, 2020 at 19:03 | history | edited | YCor | CC BY-SA 4.0 |
formatting (the question was bumped anyway)
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| Oct 7, 2019 at 2:44 | comment | added | Master | This wrong. We can't get $M_{j(\alpha)}\subseteq M$ from $M^\alpha\subseteq M$; we can only get it from $M^{j(\alpha)}\subseteq M$. For this reason, the least supercompact cardinal is not $1$-extendible, but is a stationary limit of cardinals that $1$-extendible. | |
| Jun 20, 2019 at 19:55 | answer | added | Master | timeline score: 3 | |
| Nov 4, 2013 at 8:13 | history | edited | Everett Piper | CC BY-SA 3.0 |
Some remarks on the relationship of extendibles to supercompacts and the Sigma_n correctness of these cardinals.
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| Nov 4, 2013 at 7:36 | history | edited | Everett Piper | CC BY-SA 3.0 |
changed notation about iteration to composition
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| Nov 4, 2013 at 7:04 | comment | added | Rachid Atmai | ...$j(\kappa)>\delta$ and if $P_{\kappa}(\delta) \subset V_{\theta}$. I'm not sure about it and in any case you are asking about the sup of the critical sequence. | |
| Nov 4, 2013 at 7:04 | comment | added | Rachid Atmai | If $\kappa=crit(j)$ is $\theta$-supercompact for some $\theta$ and if we let $j:V \to M$ witness this $\theta$- supercompactness then since $j|V_{\alpha}: V_{\alpha} \to j(V_{\alpha})= M_{j(\alpha)}$ is bounded by $\theta$ so it is in $M$, by the supercompactness, we get that $\kappa$ is $\alpha$-extendible for any $\alpha$ such that $\beth_{\alpha} \leq \theta$. We can get the appropriate supercompactness from embeddings $j:V_{\theta} \to V_{\theta}$, say by $X \in \mu \leftrightarrow j"\delta \in j(X)$ with $X \subset P_{\kappa}(\delta)$ if... | |
| Nov 4, 2013 at 5:36 | history | asked | Everett Piper | CC BY-SA 3.0 |