Large cardinals and definable counterexamples to the continuum hypothesis Original Research Article

In this paper we consider whether View the MathML source 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 View the MathML source 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 Changʹs conjecture.