Let χ be the minimum cardinality of a subset of that cannot be made convergent by multiplication with a single Toeplitz matrix. By an application of a creature forcing we show that < χ is consistent. We thus answer a question by Vojtáš. We give two kinds of models for the strict inequality. The first is the combination of an ℵ₂-iteration of some proper forcing with adding ℵ₁ random reals. The second kind of models is obtained by adding δ random reals to a model of for some δ ∈ [ℵ₁,κ). It was a conjecture of Blass that = ℵ₁ < χ = κ holds in such a model. For the analysis of the second model we again use the creature forcing from the first model.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm171-2-4,
author = {Heike Mildenberger and Saharon Shelah},
title = {The splitting number can be smaller than the matrix chaos number},
journal = {Fundamenta Mathematicae},
volume = {173},
year = {2002},
pages = {167-176},
zbl = {0992.03058},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm171-2-4}
}
Heike Mildenberger; Saharon Shelah. The splitting number can be smaller than the matrix chaos number. Fundamenta Mathematicae, Tome 173 (2002) pp. 167-176. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm171-2-4/