Timeline for What large cardinals are needed to imply projective sets have the perfect set property?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 30, 2023 at 15:24 | comment | added | Julia Williams | @FarmerS Thanks for the answer! If you want to write it as an answer instead of a comment I can accept it. | |
| Jan 29, 2023 at 1:37 | comment | added | Asaf Karagila♦ | @Farmer: So, more or less Con(ZFC+PD), right? | |
| Jan 27, 2023 at 23:22 | comment | added | Farmer S | But "infinitely many Woodins" is certainly overkill, even for projective determinacy. By well known results, for that it suffices to have that for every $n<\omega$, $M_n^{\#}$ exists and is $\omega_1$-iterable. | |
| Jan 27, 2023 at 23:16 | comment | added | Farmer S | Finitely many Woodins is not enough, because in $M_n$ (the minimal iterable proper class model with $n<\omega$ Woodin cardinals) it fails. | |
| Jan 27, 2023 at 21:48 | comment | added | Hanul Jeon | Schindler and Wilson proved that the consistency strength of $\mathsf{ZFC}$ with the perfect set property for universally Baire sets is equal to $\mathsf{ZFC}$ with a large cardinal called virtually Shelah cardinal, whose consistency strength is below $0^\sharp$. It does not answer your question, but might be relevant. | |
| Jan 27, 2023 at 16:03 | history | asked | Julia Williams | CC BY-SA 4.0 |