## Tagged Questions

3answers
498 views

### Counterintuitive consequences of the Axiom of Determinacy?

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 …
1answer
182 views

### Which forcings preserve (some) determinacy?

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 …
2answers
265 views

### Weakly homogeneous trees under AD

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 …
1answer
183 views

### sigma-algebra generated by OD sets

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? …
2answers
622 views

### How additive is Lebesgue measure in ZF+AD ?

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 : …
0answers
318 views

### How to prove projective determinacy (PD) from I0?

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 …
1answer
300 views

### Consistency strengths related to the perfect set property

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 …
2answers
653 views

### Martin’s cone theorem and recursion theory

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 …
1answer
253 views

### value of Theta in ZF+AD

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 …
1answer
164 views

### The projection of a weakly homogeneous tree is determined

Where can I read a proof of this?
1answer
205 views

### Related Open Game in Analytic Determinacy

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 …
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