Random trees under CH
 James Hirschorn
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We extend Jensen’s Theorem that Souslin’s Hypothesis is consistent with CH, by showing that the statement Souslin’s Hypothesis holds in any forcing extension by a measure algebra is consistent with CH. We also formulate a variation of the principle (*) (see [AT97], [Tod00]) for closed sets of ordinals, and show its consistency relative to the appropriate large cardinal hypothesis. Its consistency with CH would extend Silver’s Theorem that, assuming the existence of an inaccessible cardinal, the failure of Kurepa’s Hypothesis is consistent with CH, by its implication that the statement Kurepa’s Hypothesis fails in any forcing extension by a measure algebra is consistent with CH.
 Title
 Random trees under CH
 Journal

Israel Journal of Mathematics
Volume 157, Issue 1 , pp 123153
 Cover Date
 20070101
 DOI
 10.1007/s1185600600053
 Print ISSN
 00212172
 Publisher
 SpringerVerlag
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 Authors

 James Hirschorn ^{(1)}
 Author Affiliations

 1. Department of Mathematics, University of Toronto, Canada