The splitting number can be smaller than the matrix chaos number

by Mildenberger and Shelah. [MdSh:753]
Fundamenta Math, 2002
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 s < chi is consistent. We thus answer a question by Vojtas. 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 MA_{< kappa} for some delta in [aleph_1, kappa) . It was a conjecture of Blass that 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.


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