# Sh:753

• Mildenberger, H., & Shelah, S. (2002). The splitting number can be smaller than the matrix chaos number. Fund. Math., 171(2), 167–176.
• Abstract:
Let \chi be the minimum cardinal of a subset of 2^\omega that cannot be made convergent by multiplication with a single Toeplitz matrix. By an application of creature forcing we show that {\mathfrak s}<\chi 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 \aleph_2-iteration of some proper forcing with adding \aleph_1 random reals. The second kind of models is got by adding \delta random reals to a model of {\rm MA}_{<\kappa} for some \delta\in [\aleph_1,\kappa). It was a conjecture of Blass that {\mathfrak s}=\aleph_1<\chi= \kappa holds in such a model. For the analysis of the second model we again use the creature forcing from the first model.
• Version 2001-05-27_11 (9p) published version (10p)
Bib entry
@article{Sh:753,
author = {Mildenberger, Heike and Shelah, Saharon},
title = {{The splitting number can be smaller than the matrix chaos number}},
journal = {Fund. Math.},
fjournal = {Fundamenta Mathematicae},
volume = {171},
number = {2},
year = {2002},
pages = {167--176},
issn = {0016-2736},
mrnumber = {1880382},
mrclass = {03E17 (03E35)},
doi = {10.4064/fm171-2-4},
note = {\href{https://arxiv.org/abs/math/0011188}{arXiv: math/0011188}},
arxiv_number = {math/0011188}
}