I just read Dr Strangechoice's explanation that if all subsets of the real numbers are Lebesgue measurable, then you can partition $2^\omega$ into more than $2^\omega$ many pairwis …

The question is exactly as in the title. I'm interested in general in all questions of the form "which forcings preserve property P?" for any P, but determinacy assumptions occupy …

If AD$_\mathbb{R}$ holds and $\kappa < \Theta$ then every tree $T$ on $\kappa$ is weakly homogeneous (Martin–Woodin, "Weakly homogeneous trees.") I recall hearing that the hypo …

Assume $V=L(\mathbb{R})$ and the Axiom of Determinacy. Is every set of reals generated by ordinal-definable sets of reals under the operations of countable union and intersection? …

What is known about the additivity of Lebesgue measure under the Axiom of Determinacy? That is, for what cardinals $\kappa$ do we have with $|I| = \kappa$, for all functions $f : …

Martin and Steel (in 1987?) showed that if there are infinite many Woodin cardinals then every projective set of reals is determined (PD). However, it is mentioned in many texts th …

I want a model of $\mathrm{MA}_{\sigma\mathrm{-centered}}+\neg\mathrm{CH}$ in which every set of reals in $L(\mathbb{R})$ has the perfect set property. In terms of consistency stre …

Martin's remarkable cone theorem in the theory of determinacy says the following: Suppose $A\subseteq \omega^\omega$ is Turing invariant and determined. If $\forall x\exists y …

Since I found out about it, I've always been interested in the Axiom of Determinacy rather than the Axiom of Choice. Along these lines, I've kept flipping back to http://en.wikipe …

Where can I read a proof of this?

For this question, please refer to Chapter 33 page 638, Set Theory Millennium Edition, by Thomas Jech. The proof of analytic games $G_A$ is converted into an open game $G^\ast$ on …