The splitting number can be smaller than the matrix chaos number

Heike Mildenberger; Saharon Shelah

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The splitting number can be smaller than the matrix chaos number

Heike Mildenberger·Saharon Shelah

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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 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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BibTeX RIS

Heike Mildenberger, Saharon Shelah. 2000-11-22. The splitting number can be smaller than the matrix chaos number. https://arxiv.org/abs/math/0011188

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