Some applications of coarse inner model theory

Journal of Symbolic Logic 62 (2):337-365 (1997)
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Abstract

The Martin-Steel coarse inner model theory is employed in obtaining new results in descriptive set theory. $\underset{\sim}{\Pi}$ determinacy implies that for every thin Σ 1 2 equivalence relation there is a Δ 1 3 real, N, over which every equivalence class is generic--and hence there is a good Δ 1 2 (N ♯ ) wellordering of the equivalence classes. Analogous results are obtained for Π 1 2 and Δ 1 2 quasilinear orderings and $\underset{\sim}{\Pi}^1_2$ determinacy is shown to imply that every Π 1 2 prewellorder has rank less than $\underset{\sim}{\delta}^1_2$

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Citations of this work

Thin equivalence relations in scaled pointclasses.Ralf Schindler & Philipp Schlicht - 2011 - Mathematical Logic Quarterly 57 (6):615-620.
Thin equivalence relations and inner models.Philipp Schlicht - 2014 - Annals of Pure and Applied Logic 165 (10):1577-1625.

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References found in this work

Set Theory.Keith J. Devlin - 1981 - Journal of Symbolic Logic 46 (4):876-877.
Descriptive Set Theory.Yiannis Nicholas Moschovakis - 1982 - Studia Logica 41 (4):429-430.
HOD L(ℝ) is a Core Model Below Θ.John R. Steel - 1995 - Bulletin of Symbolic Logic 1 (1):75-84.
On the determinacy of games on ordinals.L. A. Harrington - 1981 - Annals of Mathematical Logic 20 (2):109.
The consistency strength of projective absoluteness.Kai Hauser - 1995 - Annals of Pure and Applied Logic 74 (3):245-295.

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