Timeline for Forcing over models without the axiom of choice
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 10, 2018 at 16:35 | answer | added | Thomas Benjamin | timeline score: 2 | |
| Oct 2, 2011 at 0:23 | answer | added | Andreas Blass | timeline score: 6 | |
| Sep 28, 2011 at 7:04 | comment | added | Asaf Karagila♦ | Andres, many thanks for putting time. However the two questions are just examples of forcing related theorems in the choiceless context. I am looking for a good place to start with such theorems, if it exists. | |
| Sep 28, 2011 at 6:50 | comment | added | Andrés E. Caicedo | Hi Asaf, Only now I see this nice question. Busy life as usual, but I'll add something of substance if time permits. For now, the answer to 1 is no. Gitik's model where all cardinals are singular is a counterexample. Woodin has shown that in the choiceless setting, from very strong large cardinal assumptions (beyond embeddings from V to V) it follows that we can recover choice, but class forcing is needed in general. It would be fabulous if one could provide structure in Woodin's setting by identifying enough of it as a symmetric model. But V is in general a class symmetric extension of HOD. | |
| Sep 27, 2011 at 17:28 | answer | added | François G. Dorais | timeline score: 3 | |
| Sep 27, 2011 at 15:08 | history | edited | Asaf Karagila♦ | CC BY-SA 3.0 |
Added on the original intent.
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| Sep 26, 2011 at 18:52 | answer | added | Noah Schweber | timeline score: 8 | |
| Sep 26, 2011 at 18:08 | history | edited | Asaf Karagila♦ | CC BY-SA 3.0 |
Theorems about forcing.
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| Sep 26, 2011 at 18:08 | comment | added | Asaf Karagila♦ | Ricky, I was referring to forcing related theorems. Not general theorems. I will add this to the question for it to be clearer. | |
| Sep 26, 2011 at 18:03 | comment | added | user5810 | "or with the relation between theorems proved in ZFC and the amount of choice needed for them to hold." | |
| Sep 26, 2011 at 17:54 | answer | added | Péter Komjáth | timeline score: 5 | |
| Sep 26, 2011 at 16:32 | comment | added | Asaf Karagila♦ | @Ricky: Are you sure? This is about consequences of AC, while I am looking for defining forcing in the lack thereof. | |
| Sep 26, 2011 at 16:10 | comment | added | Not Mike | (retracted, was looking at the wrong paper.) | |
| Sep 26, 2011 at 15:42 | comment | added | user5810 | Well, the canonical reference is books.google.com/…. | |
| Sep 26, 2011 at 15:37 | history | asked | Asaf Karagila♦ | CC BY-SA 3.0 |