Blog Archives

Proxy principles in combinatorial set theory

Joint work with Ari Meir Brodsky and Shira Yadai. Abstract. The parameterized proxy principles were introduced by Brodsky and Rinot in a 2017 paper as new foundations for the construction of κ-Souslin trees in a uniform way that does not … Continue reading

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

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

Full Souslin trees at small cardinals

Joint work with Shira Yadai and Zhixing You. Abstract. A κ-tree is full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full κ-Souslin tree may consistently exist. Shelah gave an affirmative … Continue reading

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