Timeline for Why the restrictions in the definition of Berkeley cardinals?
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 3, 2019 at 21:45 | vote | accept | Zuhair Al-Johar | ||
| Jan 2, 2019 at 19:25 | comment | added | Wojowu | I think assuming the condition for every class doesn't immediately lead to a contradiction, but it might increase the strength of the notion - suppose there is an inaccessible $\lambda$ above a Berkeley $\kappa$. Consider $V_\lambda$ - every class in it is a set in $V$, and an elementary embedding from it to itself is again a class in $V_\lambda$, so $V_\lambda$ satisfies the Berkeley condition for all classes. One reason for restricting the definition to sets is that it turns the notion into something expressible in ZF - you can't quantify, not even explicitly talk about, classes there. | |
| Jan 2, 2019 at 18:55 | answer | added | Noah Schweber | timeline score: 5 | |
| Jan 2, 2019 at 18:43 | history | asked | Zuhair Al-Johar | CC BY-SA 4.0 |