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September 2004 Solovay models and forcing extensions
Joan Bagaria, Roger Bosch
J. Symbolic Logic 69(3): 742-766 (September 2004). DOI: 10.2178/jsl/1096901764

Abstract

We study the preservation under projective ccc forcing extensions of the property of L(ℝ) being a Solovay model. We prove that this property is preserved by every strongly-Σ31 absolutely-ccc forcing extension, and that this is essentially the optimal preservation result, i.e., it does not hold for δ31 absolutely-ccc forcing notions. We extend these results to the higher projective classes of ccc posets, and to the class of all projective ccc posets, using definably-Mahlo cardinals. As a consequence we obtain an exact equiconsistency result for generic absoluteness under projective absolutely-ccc forcing notions.

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Joan Bagaria. Roger Bosch. "Solovay models and forcing extensions." J. Symbolic Logic 69 (3) 742 - 766, September 2004. https://doi.org/10.2178/jsl/1096901764

Information

Published: September 2004
First available in Project Euclid: 4 October 2004

zbMATH: 1070.03031
MathSciNet: MR2078919
Digital Object Identifier: 10.2178/jsl/1096901764

Subjects:
Primary: 03E15, 03E35

Rights: Copyright © 2004 Association for Symbolic Logic

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Vol.69 • No. 3 • September 2004
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