## Journal of Symbolic Logic

### Homogeneously Suslin sets in tame mice

Farmer Schlutzenberg

#### Abstract

This paper studies homogeneously Suslin (hom) sets of reals in tame mice. The following results are established: In $0$ the hom sets are precisely the $\underset{\widetilde{}}{\Pi^1_1}$ sets. In $M_n$ every hom set is correctly $\underset{\widetilde{}}{\Delta^1_{n+1}}$, and $(\delta+1)$-universally Baire where $\delta$ is the least Woodin. In $M_\omega$ every hom set is $< \lambda$-hom, where $\lambda$ is the supremum of the Woodins.

#### Article information

Source
J. Symbolic Logic Volume 77, Issue 4 (2012), 1122-1146.

Dates
First available in Project Euclid: 15 October 2012

http://projecteuclid.org/euclid.jsl/1350315579

Digital Object Identifier
doi:10.2178/jsl.7704040

Mathematical Reviews number (MathSciNet)
MR3051617

Zentralblatt MATH identifier
06122627

#### Citation

Schlutzenberg, Farmer. Homogeneously Suslin sets in tame mice. J. Symbolic Logic 77 (2012), no. 4, 1122--1146. doi:10.2178/jsl.7704040. http://projecteuclid.org/euclid.jsl/1350315579.