Timeline for Models of ZF intermediate between a model of ZFC and a generic extension
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Jan 24, 2020 at 2:56 | history | became hot network question | |||
| Jan 23, 2020 at 19:55 | comment | added | Andrés E. Caicedo | @Toby I edited $M[x]$ to $M(x)$. In modern notation, the former is by design a model of choice, so it would be confusing to use it in this setting. | |
| Jan 23, 2020 at 19:54 | history | edited | Andrés E. Caicedo | CC BY-SA 4.0 |
edited body
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| Jan 23, 2020 at 19:25 | vote | accept | Toby Meadows | ||
| Jan 23, 2020 at 19:19 | answer | added | Asaf Karagila♦ | timeline score: 10 | |
| Jan 23, 2020 at 19:16 | history | edited | Toby Meadows | CC BY-SA 4.0 |
added 59 characters in body
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| Jan 23, 2020 at 19:14 | comment | added | Toby Meadows | Hmmm .. I'll edit the question and see if you still think it's solved. Thanks for looking at it. | |
| Jan 23, 2020 at 19:12 | comment | added | Asaf Karagila♦ | Toby, a Cohen real is the most basic of generic extensions... | |
| Jan 23, 2020 at 19:12 | comment | added | Toby Meadows | Thanks. I was aware of this result and had it in mind, but I'm not sure it does answer the question. This is why I added the condition that M[G] is a generic extension of M. Grigorieff's Theorem B shows that in such a case N=M[x] for some x \in N. If I understand the remarks on the Bristol model correctly, then it cannot be of the form M[x] (assuming that L=M). I probably should have mentioned the Theorem B think in the OP. | |
| Jan 23, 2020 at 18:57 | comment | added | Andrés E. Caicedo | The answer is no! For a rather dramatic example, see for instance MR3878470 Karagila, Asaf The Bristol model: an abyss called a Cohen real. J. Math. Log. 18 (2018), no. 2, 1850008, 37 pp. (Take a look at section 7.2 for a brief comment on this matter.) | |
| Jan 23, 2020 at 18:42 | history | asked | Toby Meadows | CC BY-SA 4.0 |