Geodesic
On a problem of Steve Kalikow
Fundamenta Mathematicae, Tome 166 (2000) no. 1, pp. 137-151.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm-166-1-2-137-151
Mots-clés : set theory, forcing, continuity, Kalikow, free subset

Saharon Shelah 1

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Saharon Shelah. On a problem of Steve Kalikow. Fundamenta Mathematicae, Tome 166 (2000) no. 1, pp. 137-151. doi : 10.4064/fm-166-1-2-137-151. http://geodesic.mathdoc.fr/articles/10.4064/fm-166-1-2-137-151/

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