Timeline for Where does this strengthening of I1 stand?
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
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| Jun 7, 2017 at 14:58 | vote | accept | Joseph Van Name | ||
| May 5, 2017 at 23:07 | answer | added | Gabe Goldberg | timeline score: 7 | |
| S Feb 13, 2017 at 22:54 | history | bounty ended | CommunityBot | ||
| S Feb 13, 2017 at 22:54 | history | notice removed | CommunityBot | ||
| S Feb 5, 2017 at 20:48 | history | bounty started | Joseph Van Name | ||
| S Feb 5, 2017 at 20:48 | history | notice added | Joseph Van Name | Draw attention | |
| S Feb 5, 2017 at 6:01 | history | bounty ended | CommunityBot | ||
| S Feb 5, 2017 at 6:01 | history | notice removed | CommunityBot | ||
| Feb 4, 2017 at 6:55 | comment | added | Joseph Van Name | The I1-tower cardinals also seem to help produce interesting algebras of elementary embeddings. For example, if $A$ is a linear ordering of $V_{\delta}$, then $A$ induces compatible linear orderings on certain finite quotients of algebras of elementary embeddings. Without something like I1-tower cardinals, one has to resort to working within forcing extensions in order to obtain compatible linear orderings. | |
| Jan 28, 2017 at 4:40 | history | edited | Joseph Van Name | CC BY-SA 3.0 |
added 92 characters in body
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| S Jan 28, 2017 at 4:39 | history | bounty started | Joseph Van Name | ||
| S Jan 28, 2017 at 4:39 | history | notice added | Joseph Van Name | Draw attention | |
| May 17, 2015 at 22:53 | comment | added | Joseph Van Name | I chose this axiomatization since the I1-tower cardinals are a modification to the notion of a Vopenka cardinal. Recall that a cardinal $\delta$ is a Vopenka cardinal if and only if whenever $A\subseteq V_{\delta}$ there is a $\kappa<\delta$ such that if $\kappa<\alpha<\delta$ there is some elementary embedding $j:\langle V_{\mu},\in,A\cap V_{\mu}\rangle\rightarrow\langle V_{\lambda},\in,A\cap V_{\lambda}\rangle$ with $\lambda,\mu<\delta$,$crit(j)=\kappa$, and $j(\kappa)>\alpha$. Therefore every I1-tower cardinal is a Vopenka cardinal and a limit of I1 cardinals. | |
| May 17, 2015 at 22:52 | comment | added | Joseph Van Name | Everett Piper. I simply wanted to extend the notion of an I1 cardinal to a larger cardinal with more consistency strength without resorting to models that necessarily look like L as one has with I0 cardinals, so I want to see what reasonable strengthenings of I1 are possible. | |
| May 17, 2015 at 3:15 | comment | added | Everett Piper | @Joseph: Can I ask what the motivation is for this axiom? I think your subsets A cannot contain any member of the critical sequence, or maybe just \kappa, the critical point itself. Maybe there are other subsets that can't be preserved either? | |
| May 16, 2015 at 13:25 | comment | added | Joseph Van Name | Victoria. Yes. That is what I meant. Thanks for pointing that out. | |
| May 16, 2015 at 13:24 | history | edited | Joseph Van Name | CC BY-SA 3.0 |
edited body
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| May 16, 2015 at 13:01 | comment | added | Victoria Gitman | Did you mean $A\subseteq V_\delta$ and later $\lambda<\delta$? | |
| May 16, 2015 at 12:52 | history | asked | Joseph Van Name | CC BY-SA 3.0 |