Homogeneously Suslin sets in tame mice

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

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.

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Permanent link to this document: http://projecteuclid.org/euclid.jsl/1350315579
Digital Object Identifier: doi:10.2178/jsl.7704040
Zentralblatt MATH identifier: 06122627
Mathematical Reviews number (MathSciNet): MR3051617

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