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On a problem of Steve Kalikow

100%

Shelah S.

Fundamenta Mathematicae

2000

tom 166

nr 1-2

137-151

The Kalikow problem for a pair (λ,κ) of cardinal numbers,λ > κ (in particular κ = 2) is whether we can map the family of ω-sequences from λ to the family of ω-sequences from κ in a very continuous manner. Namely, we demand that for η,ν ∈ ω we have: η, ν are almost equal if and only if their images are. We show consistency of the negative answer, e.g., for $ℵ_ω$ but we prove it for smaller cardinals. We indicate a close connection with the free subset property and its variants.

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1 Fundamenta Mathematicae

1 Shelah S.

1 2000

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On a problem of Steve Kalikow