Colouring and non-productivity of aleph2-cc
Saharon Shelah
Abstract
We prove that colouring of pairs from aleph2 with strong properties exists. The easiest to state (and quite a well known problem) it solves: there are two topological spaces with cellularity aleph1 whose product has cellularity aleph2 ; equivalently we can speak on cellularity of Boolean algebras or on Boolean algebras satisfying the aleph2-c.c. whose product fails the aleph2-c.c. We also deal more with guessing of clubs.
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