Timeline for Transfinite recursion, collection and replacement in KP and KF
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 4, 2013 at 6:21 | comment | added | Philip Welch | I agree with Joel's comment concerning ITTM's in L. In L the Collection vis a vis Replacement concern is not an issue as there is a global wellorder of L. @Joel: thanks for clarifying the status of the $\aleph_n$'s in my answer. | |
| Aug 4, 2013 at 0:19 | comment | added | Joel David Hamkins | The recursion defining the operation of ITTMs does not seem to be affected by the replacement/collection issue, since one may undertake it inside the constructible universe $L$. | |
| Aug 3, 2013 at 19:42 | vote | accept | Frode Alfson Bjørdal | ||
| Aug 3, 2013 at 19:41 | comment | added | Frode Alfson Bjørdal | I am concerned with a construction which is strongly related to your infinite time Turing machines. Are they affected? | |
| Aug 3, 2013 at 19:13 | vote | accept | Frode Alfson Bjørdal | ||
| Aug 3, 2013 at 19:13 | |||||
| Aug 3, 2013 at 16:59 | comment | added | Joel David Hamkins | By $\aleph_k$ here, one should understand the $\aleph_k$'s of a ground model, which have all been collapsed to $\omega$ by forcing. The old $\aleph_\omega$ becomes the new $\omega_1$, which is singular in our model, even though it satisfies ZFC- and, in particular, the axiom of choice. | |
| Aug 3, 2013 at 15:29 | history | answered | Philip Welch | CC BY-SA 3.0 |