# Sh:753

- Mildenberger, H., & Shelah, S. (2002).
*The splitting number can be smaller than the matrix chaos number*. Fund. Math.,**171**(2), 167–176. arXiv: math/0011188 DOI: 10.4064/fm171-2-4 MR: 1880382 -
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. - 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}, doi = {10.4064/fm171-2-4}, mrclass = {03E17 (03E35)}, mrnumber = {1880382}, mrreviewer = {P\'eter Komj\'ath}, doi = {10.4064/fm171-2-4}, note = {\href{https://arxiv.org/abs/math/0011188}{arXiv: math/0011188}}, arxiv_number = {math/0011188} }