Timeline for Can Friedman's property fail at or above a supercompact cardinal?

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May 16 at 8:18	comment	added	Hannes Jakob		Thank you very much! Do you know perchance why this is still listed as one of the problems, despite other problems being updated to show their resolution?
May 16 at 8:08	comment	added	Chris Lambie-Hanson		To see why $FP_\kappa$ fails after forcing with $\mathrm{Coll}(\omega, \omega_1)$: work in $M$, and let $\dot{f}$ be a name for a continuous, increasing map from $\omega_2^M$ to $A_\kappa$. Then we can find a single condition $p$ that decides the value of $\dot{f}(\alpha)$ for cofinally many $\alpha < \omega_2^M$. But since $\dot{f}$ is forced to be continuous, $p$ actually decides the value of $\dot{f}$ on a club, so we have a closed subset of order type $\omega_2^M$ inside $A_\kappa$ in $M$ itself, which is a contradiction.
May 15 at 19:14	history	answered	Hannes Jakob	CC BY-SA 4.0