Tag Archives: regressive Souslin tree

The vanishing levels of a tree

Joint work with Shira Yadai and Zhixing You. Abstract. We initiate the study of the spectrum of sets that can be realized as the vanishing levels V(T) of a normal κ-tree T. This is an invariant in the … Continue reading

Posted in Preprints, Souslin Hypothesis | Tagged , , , , , , , , | 1 Comment

A guessing principle from a Souslin tree, with applications to topology

Joint work with Roy Shalev. Abstract. We introduce a new combinatorial principle which we call AD. This principle asserts the existence of a certain multi-ladder system with guessing and almost-disjointness features, and is shown to be sufficient for carrying out … Continue reading

Posted in Publications, Souslin Hypothesis, Topology | Tagged , , , , , , | 2 Comments

Higher Souslin trees and the GCH, revisited

Abstract.  It is proved that for every uncountable cardinal λ, GCH+◻(λ+) entails the existence of a cf(λ)-complete λ+-Souslin tree. In particular, if GCH holds and there are no 2-Souslin trees, then 2 is weakly compact in Godel’s constructible universe, improving … Continue reading

Posted in Publications, Souslin Hypothesis | Tagged , , , , , , , | 16 Comments