On Arhangelskii's Problem

Mathematics – Logic

Scientific paper

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Scientific paper

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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