Isomorphisms of countable factors
The purpose of this section is to show (following Hanf, as simplified, orally, by Dana Scott) that there exist countable Boolean algebras A and B such that A =A × B × B but A ≠ A × B. The method of attack is topological; in fact, we shall construct Boolean spaces X and Y, each with a countable base, so that X = X + Y + Y but X ≠ X + Y. (The equal sign denotes homeomorphism here.)
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