# Random trees under CH

Article

- Received:
- Revised:

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

- 6 Citations
- 73 Downloads

## 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