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Abstract

We investigate $||χ_\mathbb A,2||$, the minimum cardinality of a subset of $2^ω$ that cannot be made convergent by multiplication with a single matrix taken from $\mathbb A$, for different sets $\mathbb A$ of Toeplitz matrices, and show that for some sets $\mathbb A$ it coincides with the splitting number. We show that there is no Galois-Tukey connection from the chaos relation on the diagonal matrices to the chaos relation on the Toeplitz matrices with the identity on $2^ω$ as first component. With Suslin c.c.c. forcing we show that $||χ_\mathbb M,2||$ < $\gb ∙ \gs$ is consistent relative to ZFC.