Optimal matrices of partitions and an application to Souslin trees

Tom 210 / 2010

Gido Scharfenberger-Fabian Fundamenta Mathematicae 210 (2010), 111-131 MSC: Primary 03E05; Secondary 05A18. DOI: 10.4064/fm210-2-2


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.


  • Gido Scharfenberger-FabianInstitute of Mathematics and Computer Sciences
    Walther-Rathenau-Strasse 47
    17487 Greifswald, Germany

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