Timeline for Is axiom of constructibility $V = L$ consistent with Tarski–Grothendieck set theory?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 29, 2020 at 15:14 | history | edited | Andrés E. Caicedo | CC BY-SA 4.0 |
edited body
|
| Oct 29, 2020 at 5:57 | comment | added | Hanul Jeon | @Noah Thank you for your comment. I fixed that part of my answer. | |
| Oct 29, 2020 at 5:56 | comment | added | Noah Schweber | Again for the OP: to see that inaccessibility is not upwards absolute, consider forcings of the form $Col(\omega,\kappa)$ (say). | |
| Oct 29, 2020 at 5:55 | history | edited | Hanul Jeon | CC BY-SA 4.0 |
Fix some error
|
| Oct 29, 2020 at 5:46 | comment | added | Noah Schweber | +1. For the OP re: absoluteness: inaccessibility is more generally downwards absolute since it is a $\Pi_1$ property. All the "small" large cardinal properties (inaccessibility, Mahlo, weakly compact, ...) are similar. Things change drastically once we get to measurable cardinals: while to the best of our knowledge ZFC + "There is a measurable cardinal" is consistent, ZFC + V=L proves that there is no measurable cardinal. So measurability is not downwards-absolute: even if kappa is measurable in V, kappa won't be measurable in L. | |
| Oct 29, 2020 at 5:32 | history | edited | Hanul Jeon | CC BY-SA 4.0 |
added 8 characters in body
|
| S Oct 29, 2020 at 5:27 | history | answered | Hanul Jeon | CC BY-SA 4.0 | |
| S Oct 29, 2020 at 5:27 | history | made wiki | Post Made Community Wiki by Hanul Jeon |