The splitting number can be smaller than the matrix chaos number

• Autorzy: Heike Mildenberger , Saharon Shelah
• Języki publikacji: 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.

Kategorie tematyczne

• 03E17: Cardinal characteristics of the continuum
• 03E15: Descriptive set theory
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2002
• Tom: 171
• Numer: 2
• Strony: 167-176

Daty

wydano

2002

Twórcy

autor

Heike Mildenberger

• Institut für formale Logik, Universität Wien, Währinger Str. 25, A-1090 Vienna, Austria

autor

Saharon Shelah

• Institute of Mathematics, The Hebrew University of Jerusalem, Givat Ram, 91904 Jerusalem, Israel

Identyfikatory

DOI

10.4064/fm171-2-4