## 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:

 3e+50 Continuum hypothesis and Martin’s axiom 3e+55 Large cardinals
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### References:

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