Timeline for Inner models from highly saturated ideals
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Dec 17, 2020 at 12:52 | comment | added | Monroe Eskew | @GabeGoldberg Could you send me your new email address? Your old one is bouncing. | |
| Dec 9, 2020 at 9:00 | history | edited | Monroe Eskew | CC BY-SA 4.0 |
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| Dec 5, 2020 at 10:20 | history | edited | Monroe Eskew | CC BY-SA 4.0 |
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| Nov 28, 2020 at 22:58 | history | edited | Monroe Eskew | CC BY-SA 4.0 |
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| Nov 28, 2020 at 22:56 | comment | added | Monroe Eskew | @GabeGoldberg Thanks, I will constrain the question. | |
| Nov 28, 2020 at 22:04 | comment | added | Gabe Goldberg | Having completeness exactly $\kappa$ is still not a strong enough constraint: if $\kappa$ and $\theta$ carry uniform $\kappa$-complete (resp. $\theta$-complete) ideals $I$ and $J$, you can get a countably saturated uniform ideal on $\theta$ with completeness $\kappa$ by forcing with $I$ to get $G$, then with the ideal generated by $J$ to get $H$, then taking the ideal in $V$ of sets $A$ with $[\text{id}]_G + [\text{id}]_H\notin j_H(j_G(A))$ forced by 1. (Countable saturation uses that $V[G][H]$ is a ccc extension by Jech 22.32.) | |
| Nov 28, 2020 at 20:57 | history | edited | Monroe Eskew | CC BY-SA 4.0 |
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| Nov 28, 2020 at 20:28 | comment | added | Gabe Goldberg | You probably want to demand some regularity for the ideal (or $\theta=\kappa^+$), since otherwise this is true if $\theta$ is real-valued measurable. | |
| Nov 28, 2020 at 20:21 | comment | added | Yair Hayut | Foreman's paper might be relevant: "Smoke and mirrors: Combinatorial properties of small cardinals equiconsistent with huge cardinals". | |
| Nov 28, 2020 at 15:57 | history | asked | Monroe Eskew | CC BY-SA 4.0 |