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arXiv:1110.5037 [math.LO]AbstractReferencesReviewsResources

Forcing Axioms and the Continuum Hypothesis, part II: Transcending ω_1-sequences of real numbers

Justin Tatch Moore

Published 2011-10-23, updated 2012-08-03Version 2

The purpose of this article is to prove that the forcing axiom for completely proper forcings is inconsistent with the Continuum Hypothesis. This answers a longstanding problem of Shelah. The corresponding completely proper forcing which can be constructed using CH is moreover a tree whose square is special off the diagonal. While such trees had previously been constructed by Jensen and Kunen under the assumption of Jensen's diamond principle, this is the first time such a construction has been carried out using the Continuum Hypothesis.

Comments: 12 pages. fixed a few typographical errors
Categories: math.LO
Subjects: 03E50, 03E57
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