Timeline for Is diamond consistent with 2nd order PA?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 6, 2023 at 22:51 | comment | added | Joel David Hamkins | Yes, exactly. I should have mentioned it. The generic $\Diamond$-killing classes will not be definable. One can make them definable in a $\text{ZFC}^-$ model by further forcing above $\omega_1$, of course, by coding into GCH pattern or whatever, but your additional assumption that $V=L_{\omega_1}$ prevents that. | |
| Dec 6, 2023 at 19:20 | comment | added | Hanul Jeon | I thought for a minute whether your result contradicts my one, and I found that it is not: What I provided is a diamond for definable classes, and what you provided is a model of second-order set theory with the failure of $\diamondsuit$ because there are (non-definable) classes killing diamonds. | |
| Dec 6, 2023 at 13:55 | history | edited | Joel David Hamkins | CC BY-SA 4.0 |
added 331 characters in body
|
| Dec 6, 2023 at 13:43 | history | edited | Joel David Hamkins | CC BY-SA 4.0 |
added 166 characters in body
|
| Dec 6, 2023 at 13:38 | history | answered | Joel David Hamkins | CC BY-SA 4.0 |