### Colouring and non-productivity of $\aleph_2$-cc

by Shelah. [Sh:572]

Annals Pure and Applied Logic, 1997

We prove that colouring of pairs from aleph_2 with
strong properties exists. The easiest to state (and quite a well
known problem) it solves: there are two topological spaces with
cellularity aleph_1 whose product has cellularity aleph_2 ;
equivalently we can speak on cellularity of Boolean algebras or
on Boolean algebras satisfying the aleph_2-c.c. whose product
fails the aleph_2-c.c. We also deal more with guessing of
clubs.

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