Forcing axioms and the continuum hypothesis. II: Transcending \(\omega _1\)-sequences of real numbers. (English) Zbl 1312.03032

Moore, Justin Tatch

Acta Math. 210, No. 1, 173-183 (2013).

Summary: 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 S. Shelah [Fundam. Math. 166, No. 1–2, 1–82 (2000; Zbl 0966.03044)].

MSC:

03E50	Continuum hypothesis and Martin’s axiom
03E35	Consistency and independence results
03E57	Generic absoluteness and forcing axioms

Keywords:

forcing axioms; proper forcings; continuum hypothesis

Citations:

Zbl 0966.03044

References:

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