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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2002 | 171 | 2 | 167-176

## The splitting number can be smaller than the matrix chaos number

EN

### Abstrakty

EN
Let χ be the minimum cardinality of a subset of $^ω 2$ that cannot be made convergent by multiplication with a single Toeplitz matrix. By an application of a 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 obtained 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.

167-176

wydano
2002

### Twórcy

autor
• Institut für formale Logik, Universität Wien, Währinger Str. 25, A-1090 Vienna, Austria
autor
• Institute of Mathematics, The Hebrew University of Jerusalem, Givat Ram, 91904 Jerusalem, Israel