# Sh:590

• Shelah, S. (2000). On a problem of Steve Kalikow. Fund. Math., 166(1-2), 137–151.
• Abstract:
The Kalikow problem for a pair (\lambda,\kappa) of cardinal numbers, \lambda >\kappa (in particular \kappa=2) is whether we can map the family of \omega–sequences from \lambda to the family of \omega–sequences from \kappa in a very continuous manner. Namely, we demand that for \eta,\nu\in\lambda^\omega we have:

\eta,\nu are almost equal if and only if their images are.

We show consistency of the negative answer e.g. for \aleph_\omega but we prove it for smaller cardinals. We indicate a close connection with the free subset property and its variants.

• Version 1999-11-12_11 (16p) published version (15p)
Bib entry
@article{Sh:590,
author = {Shelah, Saharon},
title = {{On a problem of Steve Kalikow}},
journal = {Fund. Math.},
fjournal = {Fundamenta Mathematicae},
volume = {166},
number = {1-2},
year = {2000},
pages = {137--151},
issn = {0016-2736},
mrnumber = {1804708},
mrclass = {03E05 (03E35)},
note = {\href{https://arxiv.org/abs/math/9705226}{arXiv: math/9705226}},
arxiv_number = {math/9705226},
specialissue = {Saharon Shelah's anniversary issue}
}