All Questions

Under ZF + AD, some games are undetermined because of lack of choice. In fact, the axiom of choice is equivalent to determinacy of games of length 2. However, we can ask whether the lack of choice ...

If $M$ is HOD of a model $N$ of $\text{AD}^+ + V=L(P(ℝ))$, what kind of forcing construction in $M$ gives back such an $N$? HODs for $\text{AD}^+ + V=L(P(ℝ))$ are conjectured (and under anti-large ...

This is a spinoff of this earlier question of mine. Short version: What measures in $L(\mathbb{R})$ can be gotten from "potentially club" filters, under appropriate hypotheses? Long version: ...

While forcing is usually presented over models of ZFC, it works equally well over models of ZF (or even less). However, the general theory of forcing becomes much stranger (much like the general ...

I've recently encountered the notion of a universally Baire set, and I've tried to look at the paper by Feng, Magidor and Woodin where this notion is studied. There are several points that confuse me. ...