Timeline for Is forcing computable?
Current License: CC BY-SA 3.0
16 events
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| Dec 17, 2014 at 13:39 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
edited body
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| Dec 17, 2014 at 13:30 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
Corrected Todd-->Dan, and summarized that argument
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| Dec 17, 2014 at 13:04 | vote | accept | Wojowu | ||
| Dec 16, 2014 at 14:02 | comment | added | Joel David Hamkins | Yes, I think there is no problem with that. If we are given the $\Delta_0$ diagram of the ground model, we can compute the $\Delta_0$ diagram of a symmetric generic extension. | |
| Dec 16, 2014 at 14:01 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
Expanded and improved
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| Dec 16, 2014 at 11:48 | comment | added | Wojowu | Very interesting; just one more question: can we use similar methods to compute a symmetric model extensions? | |
| Dec 16, 2014 at 2:35 | comment | added | Joel David Hamkins | @DanTuretsky, I would urge you to write your comment as an answer, since it does answer the question that was actually asked here. Meanwhile, the related question, where one wants to compute a forcing extension $M[G]$ from an oracle for $M$, is interesting but not yet answered. | |
| Dec 16, 2014 at 0:09 | comment | added | Joel David Hamkins | @DanTuretsky That is an excellent point, Dan. Meanwhile, I do also find the question of whether one can compute a presentation of a forcing extension $M[G]$ from any presentation of $M$ also to be interesting. I suppose I have in mind also that the inclusion $M\subset M[G]$ should be computable, connecting the two presentations, but I have the feeling that this may be exactly what is too much. | |
| Dec 16, 2014 at 0:04 | comment | added | Dan Turetsky | Nice answer. Let me just add that you don't need the $\Delta_0$ diagram if you just want some model, rather than a forcing extension. By standard arguments, any model of $ZF$ has $PA$-degree, and any $PA$-degree can compute a consistent completion of $ZFC + \neg CH$ (or any other computable, consistent set of axioms). From a complete theory, one then can perform an effective Henkin construction to get the full elementary diagram of a model. | |
| Dec 15, 2014 at 22:40 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
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| Dec 15, 2014 at 22:33 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
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| Dec 15, 2014 at 22:25 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
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| Dec 15, 2014 at 21:54 | history | undeleted | Joel David Hamkins | ||
| Dec 15, 2014 at 21:54 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
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| Dec 15, 2014 at 21:50 | history | deleted | Joel David Hamkins | via Vote | |
| Dec 15, 2014 at 21:45 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |