Timeline for Is every order type of a PA model the \omega of some ZFC model?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 19, 2014 at 13:09 | comment | added | Ali Enayat | Joel: your theorem remains true with $PA$ weakened to $I\Sigma_1$ because is known that the arithmetized completeness theorem can be implemented in $I\Sigma_1$ (this is a nontrivial result, the first proof of it was given by a forcing argument of Harrington that shows that every countable model of $I\Sigma_1$ has an expansion to a model of $WKL_0$). Also, in the theorem, one can replace $ZFC$ with any of its r.e. extensions (indeed, with any r.e. extension of a very weak fragment of $ZF$, a fragment that proves that $(\omega, \in)$ is a discrete linear order). | |
| Oct 16, 2014 at 12:53 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
Improved equivalence
|
| Oct 16, 2014 at 2:40 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
added 27 characters in body
|
| Oct 16, 2014 at 1:13 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
Turned theorem into iff equivalence
|
| Oct 16, 2014 at 1:08 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
Turned theorem into iff equivalence
|
| Oct 15, 2014 at 16:37 | comment | added | Joel David Hamkins | Great! I was hoping you'd come through with a link. | |
| Oct 15, 2014 at 16:36 | comment | added | Ali Enayat | Joel: thanks for the reference to my 2009 report. A revised draft of that report now appears in the following volume, on pages 55-64: flov.gu.se/digitalAssets/1497/1497175_ideesfixes.pdf | |
| Oct 15, 2014 at 13:35 | vote | accept | M Carl | ||
| Oct 15, 2014 at 13:36 | |||||
| Oct 15, 2014 at 13:15 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
added 27 characters in body
|
| Oct 15, 2014 at 13:07 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
added 67 characters in body
|
| Oct 15, 2014 at 13:00 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
added 2531 characters in body
|
| Oct 15, 2014 at 11:57 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
deleted 1 character in body
|
| Oct 15, 2014 at 11:45 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
added 151 characters in body
|
| Oct 15, 2014 at 11:36 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |