Projective forcing

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Annals of Pure and Applied Logic 86 (3):237-266 (1997)
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Abstract

We study the projective posets and their properties as forcing notions. We also define Martin's axiom restricted to projective sets, MA, and show that this axiom is weaker than full Martin's axiom by proving the consistency of ZFC + ¬lCH + MA with “there exists a Suslin tree”, “there exists a non-strong gap”, “there exists an entangled set of reals” and “there exists κ < 20 such that 20 < 2k”

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10.1016/s0168-0072(96)00035-8

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Citations of this work

Solovay models and forcing extensions.Joan Bagaria & Roger Bosch - 2004 - Journal of Symbolic Logic 69 (3):742-766.
Proper forcing extensions and Solovay models.Joan Bagaria & Roger Bosch - 2004 - Archive for Mathematical Logic 43 (6):739-750.
The relative strengths of fragments of Martin's axiom.Joan Bagaria - 2024 - Annals of Pure and Applied Logic 175 (1):103330.
Preserving Non-null with Suslin+ Forcings.Jakob Kellner - 2006 - Archive for Mathematical Logic 45 (6):649-664.
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

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The Independence of the Continuum Hypothesis.Paul J. Cohen - 1963 - Proceedings of the National Academy of Sciences of the United States of America 50 (6):1143--8.
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Internal Cohen extensions.D. A. Martin - 1970 - Annals of Mathematical Logic 2 (2):143.
The Independence of the Continuum Hypothesis II.Paul Cohen - 1964 - Proc. Nat. Acad. Sci. USA 51 (1):105-110.

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