Optimal Matrices of Partitions and an Application to Souslin Trees

2009/12/02 by Scharfenberger-Fabian, Gido · 2 citations
#03E05 #05A18 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.0912.0431

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 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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• The power of trees
• New consequences of PFA(T^*)

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