Timeline for Undetermined games of "overdetermined" type
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 23, 2017 at 23:21 | vote | accept | Noah Schweber | ||
| Nov 13, 2017 at 22:37 | comment | added | Noah Schweber | I'm going to hold of on accepting, to see if the bound can be improved, but this is great so I've awarded the bounty. | |
| Nov 13, 2017 at 22:37 | history | bounty ended | Noah Schweber | ||
| Nov 13, 2017 at 22:37 | comment | added | Noah Schweber | @William Yes, that was the bound I got. I'm curious if it can be gotten lower. | |
| Nov 13, 2017 at 6:45 | comment | added | William | @NoahSchweber You can also find this game of Solovay presented in Chapter II of Kleinberg's book or Sherwood's notes on Determinacy. It seems to me you can write the equivalence relation as formula of the form $(\Sigma_1^1 \wedge \Pi_1^1) \vee (\Sigma_1^1 \wedge \Pi_1^1)$. Besides the $\omega_1$-many classes, you need two additional classes corresponding to who loses first. Quickly looking at your copy game, it seems that after you account for all the ways that player I and II can lose, it seems like your equivalence relation need more than one disjunctions of $(\Sigma_1^1 \wedge \Pi_1^1)$. | |
| Nov 12, 2017 at 23:15 | comment | added | Noah Schweber | Nice! How low is it in the difference hierarchy? I can't quite get it as low as $\Sigma^1_1\wedge\Pi^1_1$, which would be nice ... | |
| Nov 12, 2017 at 23:14 | history | answered | Gabe Goldberg | CC BY-SA 3.0 |