The Splitting Number Can Be Smaller than the Matrix Chaos Number
نویسنده
چکیده
Abstract. Let χ be the minimum cardinal of a subset of 2 that cannot be made convergent by multiplication with a single Toeplitz matrix. By an application of creature forcing we show that s < χ 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 א2-iteration of some proper forcing with adding א1 random reals. The second kind of models is got by adding δ random reals to a model of MA<κ for some δ ∈ [א1, κ). It was a conjecture of Blass that s = א1 < χ = κ 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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تاریخ انتشار 2000