Kurepa's hypothesis and the continuum

Keith Devlin
1975 Fundamenta Mathematicae  
Silver [5] proved that Con(ZFC + "there is an inaccessible cardinal 11 ) implies Con(ZFC + CH +"there are no Kurepa trees"). In order to obtain this result, he generically collapses an inaccessible cardinal to w 2 • Hence CH necessarily holds in his final model. In this paper we sketch Silver's proof, and then show how it can be modified to obtain a model in which there are no Kurepa trees and the continuum is anything we wish.
doi:10.4064/fm-89-1-23-31 fatcat:ou5dkl2n75grpbrhhdez2ncpre