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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