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Forcing axioms and the continuum hypothesis

✍ Scribed by Asperό, David; Larson, Paul; Moore, Justin Tatch

Book ID
120090003
Publisher
Springer Netherlands
Year
2013
Tongue
English
Weight
408 KB
Volume
210
Category
Article
ISSN
0001-5962

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Bounded forcing axioms and the continuum
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We show that bounded forcing axioms (for instance, the Bounded Proper Forcing Axiom and the Bounded Semiproper Forcing Axiom) are consistent with the existence of (!2; !2)-gaps and thus do not imply the Open Coloring Axiom. They are also consistent with Jensen's combinatorial principles for L at the

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## Abstract In this paper we study some statements similar to the Partition Principle and the Trichotomy. We prove some relationships between these statements, the Axiom of Choice, and the Generalized Continuum Hypothesis. We also prove some independence results. MSC: 03E25, 03E50, 04A25, 04A50.