Optimal Matrices of Partitions and an Application to Souslin Trees

Details Optimal Matrices of Partitions and an Application to Souslin Trees Optimal Matrices of Partitions and an Application to Souslin Trees

2009-12-02

arxiv.org/abs/0912.0431v2

Mathematics

Logic

19 pages, submitted to Fundamenta Mathematicae

Scientific paper

The basic result of this note is a statement about the existence of families of partitions of the set of natural numbers with some favourable properties, the n-optimal matrices of partitions. We use this to improve a decomposition result for strongly homogeneous Souslin trees. The latter is in turn applied to separate strong notions of rigidity of Souslin trees, thereby answering a considerable portion of a question of Fuchs and Hamkins.

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