We prove the consistency (modulo supercompact) of a negative
answer to the Cantor discontinuum partition problem 
(i.e., 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; so we try to deal with equiconsistency.