On a problem of Steve Kalikow
Shelah, Saharon
Fundamenta Mathematicae, Tome 163 (2000), p. 137-151 / Harvested from The Polish Digital Mathematics Library
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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 ℵω but we prove it for smaller cardinals. We indicate a close connection with the free subset property and its variants.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:212473 
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Shelah, Saharon. On a problem of Steve Kalikow. Fundamenta Mathematicae, Tome 163 (2000) pp. 137-151. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv166i1p137bwm/

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