# Sh:590

- Shelah, S. (2000).
*On a problem of Steve Kalikow*. Fund. Math.,**166**(1-2), 137–151. arXiv: math/9705226 MR: 1804708 -
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.

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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} }