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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm210-2-2,
author = {Gido Scharfenberger-Fabian},
title = {Optimal matrices of partitions and an application to Souslin trees},
journal = {Fundamenta Mathematicae},
volume = {209},
year = {2010},
pages = {111-131},
zbl = {1220.03046},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm210-2-2}
}
Gido Scharfenberger-Fabian. Optimal matrices of partitions and an application to Souslin trees. Fundamenta Mathematicae, Tome 209 (2010) pp. 111-131. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm210-2-2/