Large cardinals and definable counterexamples to the continuum hypothesis

Annals of Pure and Applied Logic 76 (1):47-97 (1995)

Abstract

In this paper we consider whether L(R) has “enough information” to contain a counterexample to the continuum hypothesis. We believe this question provides deep insight into the difficulties surrounding the continuum hypothesis. We show sufficient conditions for L(R) not to contain such a counterexample. Along the way we establish many results about nonstationary towers, non-reflecting stationary sets, generalizations of proper and semiproper forcing and Chang's conjecture

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References found in this work

The Independence of the Continuum Hypothesis.Paul J. Cohen - 1963 - Proceedings of the National Academy of Sciences of the United States of America 50 (6):1143--8.
Saturated Ideals.Kenneth Kunen - 1978 - Journal of Symbolic Logic 43 (1):65-76.
Reflecting Stationary Sets.Menachem Magidor - 1982 - Journal of Symbolic Logic 47 (4):755-771.
Forcing Closed Unbounded Sets.Uri Abraham & Saharon Shelah - 1983 - Journal of Symbolic Logic 48 (3):643-657.

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