Optimal matrices of partitions and an application to Souslin trees
Volume 210 / 2010
Fundamenta Mathematicae 210 (2010), 111-131
MSC: Primary 03E05; Secondary 05A18.
DOI: 10.4064/fm210-2-2
Abstract
The basic result of this note is a statement about the existence of families of partitions of the set of natural numbers with some useful 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.
