The splitting number can be smaller than the matrix chaos number
Volume 171 / 2002
Abstract
Let be the minimum cardinality of a subset of {}^\omega 2 that cannot be made convergent by multiplication with a single Toeplitz matrix. By an application of a creature forcing we show that {\frak 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 obtained 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 {\frak 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.
