Timeline for Set theoretical multiverse and truths
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 2, 2017 at 14:36 | history | edited | Thomas Benjamin | CC BY-SA 3.0 |
corrected spelling
|
| Nov 2, 2017 at 14:30 | history | edited | Thomas Benjamin | CC BY-SA 3.0 |
Added addendum for further clarification
|
| Oct 31, 2017 at 6:50 | history | edited | Thomas Benjamin | CC BY-SA 3.0 |
added phrase for clarification
|
| Oct 31, 2017 at 6:33 | history | edited | Thomas Benjamin | CC BY-SA 3.0 |
added phrases for (hopefully) added claruty
|
| Oct 31, 2017 at 6:00 | history | edited | Thomas Benjamin | CC BY-SA 3.0 |
added symbol for greater clarity
|
| Oct 30, 2017 at 16:12 | comment | added | Nik Weaver | One concern is that within any model, proofs that are of nonstandard length relative to some other model may seem to be of standard length. If you were to write out the proof of the fundamental theorem of arithmetic in PA, I'm sure it would be very long ... so could we be sure that it's not of nonstandard length in some model? I feel obliged to emphasize again that I don't speak for Joel and would be curious as to how he would answer the question. | |
| Oct 30, 2017 at 16:09 | comment | added | Nik Weaver | @ThomasBenjamin: I don't want to speak for Joel, but yes, it is also my understanding that the relativity of $\mathbb{N}$ is due to a relativity of background set theory. But that means that the concept "is a theorem of PA" varies depending on the background set theory. | |
| Oct 30, 2017 at 14:30 | comment | added | Thomas Benjamin | @AndrésE.Caicedo: I did rewrite what was in the parentheses already. Am I to presume that that editing did not correct the problem completely? Since I have errands to run, I will correct these later--don't fault me for that, please. | |
| Oct 30, 2017 at 14:20 | comment | added | Andrés E. Caicedo | Thomas, read what you wrote. | |
| Oct 30, 2017 at 13:44 | comment | added | Thomas Benjamin | @NikWeaver: In Hamkins' multiverse conception, can there be a "standard $\mathbb N$" relative to some given background set theory? As I understand it, the relativity of $\mathbb N$ is due to a relativity of background set theory, as stated in the quote from Hamkins' preprint (I know it has been published a while back) I gave in my comments. | |
| Oct 30, 2017 at 13:32 | comment | added | Nik Weaver | I think this answer and the other comments are missing the point that in Hamkins' multiverse conception (as I understand it) there is no "standard" $\mathbb{N}$. That makes the question much more subtle and philosophical. I'd like to see Joel's response. | |
| Oct 30, 2017 at 13:14 | history | edited | Thomas Benjamin | CC BY-SA 3.0 |
corrected misstatement
|
| Oct 30, 2017 at 13:08 | comment | added | Thomas Benjamin | @AndrésE.Caicedo: Correct. Where did I say it was in my answer or my comments? If you can show me I will correct (except in the comments--all of my comments were made more than five minutes ago). | |
| Oct 30, 2017 at 12:44 | comment | added | Andrés E. Caicedo | No, an interpretation is not a theory. | |
| Oct 30, 2017 at 12:29 | history | answered | Thomas Benjamin | CC BY-SA 3.0 |