Timeline for Classifying set theories whose standard models sharing the same ordinals are equal
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 15, 2023 at 4:16 | comment | added | Ali Enayat | Thank you, it is now clear. | |
| Jan 15, 2023 at 0:54 | comment | added | Dmytro Taranovsky | @AliEnayat If $M[G]⊨A$ for some $P$-generic $G$, then some condition $p$ forces $A$ (and so for $P×P$-generic $(G_1,G_2)$ below $(p,p)$, $M[G_1]$ and $M[G_2]$ are different models of $A$). | |
| Jan 14, 2023 at 23:29 | comment | added | Ali Enayat | Thanks for your answer, but it is not clear to me how the result you mentioned can be used to handle partial orders that $P$ are not homogenous. | |
| Jan 13, 2023 at 16:47 | comment | added | Dmytro Taranovsky | @AliEnayat For a countable ZFC model $M$ and a poset $P∈M$, the intersection of all $M[G]$ equals $M$. | |
| Jan 13, 2023 at 11:55 | comment | added | Ali Enayat | Do you know of a reference, or a proof-outline, for the fact asserted in the last paragraph of your answer about the impossibility of set-forcing to produce the kind of theory asked in the open question? The only reference (other than Friedman's classical paper) I know of about the open question is the abstract of Koellner's talk: maths.ox.ac.uk/node/38151 | |
| Jan 11, 2023 at 21:13 | history | edited | Dmytro Taranovsky | CC BY-SA 4.0 |
more details; formatting
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| Jan 11, 2023 at 16:36 | comment | added | Ali Enayat | This is a very nice result, whose proof deserves to be fully written up in a paper. | |
| Jan 11, 2023 at 3:01 | history | answered | Dmytro Taranovsky | CC BY-SA 4.0 |