On a problem of Steve Kalikov
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 lambdaomega we have: eta, nu are almost equal if and only if their images are. We show consistency of the negative answer e.g. for alephomega but we prove it for smaller cardinals. We indicate a close connection with the free subset property and its variants.
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