Strong Cardinals and Sets of Reals in Lω1

Mathematical Logic Quarterly 45 (3):361-369 (1999)
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Abstract

We generalize results of [3] and [1] to hyperprojective sets of reals, viz. to more than finitely many strong cardinals being involved. We show, for example, that if every set of reals in Lω is weakly homogeneously Souslin, then there is an inner model with an inaccessible limit of strong cardinals

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10.1002/malq.19990450307

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Citations of this work

The core model for almost linear iterations.Ralf-Dieter Schindler - 2002 - Annals of Pure and Applied Logic 116 (1-3):205-272.
Projective uniformization revisited.Kai Hauser & Ralf-Dieter Schindler - 2000 - Annals of Pure and Applied Logic 103 (1-3):109-153.

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References found in this work

Iteration Trees.D. A. Martin & J. R. Steel - 2002 - Bulletin of Symbolic Logic 8 (4):545-546.
The consistency strength of projective absoluteness.Kai Hauser - 1995 - Annals of Pure and Applied Logic 74 (3):245-295.
Strong cardinals in the core model.Kai Hauser & Greg Hjorth - 1997 - Annals of Pure and Applied Logic 83 (2):165-198.
Can You Take Solovay's Inaccessible Away?Saharon Shelah & Jean Raisonnier - 1989 - Journal of Symbolic Logic 54 (2):633-635.
The Core Model Iterability Problem.J. R. Steei - 2001 - Studia Logica 67 (1):124-127.

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