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Large cardinals and definable counterexamples to the continuum hypothesis. (English) Zbl 0837.03040

Authors’ summary: We consider whether \(L (\mathbb{R})\) has “enough information” to contain a counter-example to the continuum hypothesis. We believe this question provides deep insight into the difficulties surrounding the continuum hypothesis. We show sufficient conditions for \(L (\mathbb{R})\) not to contain such a counterexample. Along the way we establish many results about non-stationary towers, non-reflecting stationary sets, generalizations of proper and semiproper forcing and Chang’s conjecture.
Reviewer: A.Tauts (Tallinn)

MSC:

03E50 Continuum hypothesis and Martin’s axiom
03E55 Large cardinals
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