Journal of Symbolic Logic

Homogeneously Suslin sets in tame mice

Farmer Schlutzenberg

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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.

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

First available in Project Euclid: 15 October 2012

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

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