On a problem of Steve Kalikov
Logic
2016-09-07 v1
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.
Cite
@article{arxiv.math/9705226,
title = {On a problem of Steve Kalikov},
author = {Saharon Shelah},
journal= {arXiv preprint arXiv:math/9705226},
year = {2016}
}