Israel Journal of Mathematics

, Volume 157, Issue 1, pp 123–153

Random trees under CH

  • James Hirschorn
Article

DOI: 10.1007/s11856-006-0005-3

Cite this article as:
Hirschorn, J. Isr. J. Math. (2007) 157: 123. doi:10.1007/s11856-006-0005-3

Abstract

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.

Copyright information

© The Hebrew University of Jerusalem 2007

Authors and Affiliations

  • James Hirschorn
    • 1
  1. 1.Department of MathematicsUniversity of TorontoCanada
  2. 2.Graduate School of Science and TechnologyKobe UniversityJapan

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