### Anti--homogeneous Partitions of a Topological Space

by Shelah. [Sh:668]

Scientiae Math Japonicae, 2004

We prove the consistency (modulo supercompact) of a
negative answer to Arhangelskii's problem (some Hausdorff compact
space cannot be partitioned to two sets not containing a closed copy
of Cantor discontinuum). In this model we have CH. Without CH we
get consistency results using a pcf assumption, close relatives of
which are necessary for such results.

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