# Tagged Questions

**5**

votes

**1**answer

202 views

### $\omega$ universally Baire sets, tree representations

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.
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**9**

votes

**1**answer

154 views

### n odd: $\bf\Delta^1_n$ wadge degrees are $< \bf\delta^1_{n+1}$

My adviser is out of town and there is a comment in the Van Wesep paper "wadge degrees and descriptive set theory" that I can't figure out.
Work in ZF+AD throughout.
As stated in the title, the ...

**9**

votes

**1**answer

263 views

### Universal $(\Sigma^2_1)^{\text{Hom}_{\mathord{<}\lambda}}$ set

Does anyone know of a reference for the fact that if $\lambda$ is a limit of Woodin cardinals, then the pointclass $(\Sigma^2_1)^{\text{Hom}_{\mathord{<}\lambda}}$ is $\omega$-parameterized? By ...

**10**

votes

**1**answer

246 views

### Consistency strength of projective determinacy (PD)

Let PD stand for projective determinacy, and consider the two claims:
(1) For each n=1,2,..., Con(ZFC+PD) implies Con(ZFC + there are n Woodin cardinals)
(2) Con(ZFC+PD) implies Con(ZFC + there are ...

**10**

votes

**1**answer

232 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 a special place in ...

**3**

votes

**1**answer

210 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?
The class of sets ...

**6**

votes

**2**answers

307 views

### Weakly homogeneous trees under AD

If AD$_\mathbb{R}$ holds and $\kappa < \Theta$ then every tree $T$ on $\kappa$ is weakly homogeneous (Martinâ€“Woodin, "Weakly homogeneous trees.") I recall hearing that the hypothesis can be ...

**10**

votes

**1**answer

356 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 strength, it is known ...

**0**

votes

**1**answer

180 views

**3**

votes

**1**answer

233 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 some suitable ...