On a problem of Steve Kalikow
by Shelah. [Sh:590]
Fundamenta Math, 2000
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
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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