Isomorphisms of factors
A natural question about products of Boolean algebras (and of many other algebraic systems) is this: if each of two algebras is isomorphic to a factor of the other, does it follow that the two algebras are isomorphic. (“Factor” refers of course to the multiplication defined in §26.) The question can be reformulated and specialized in various interesting ways. For grammatical convenience we shall express the reformulations as statements rather than questions; the problem will then be to decide which statements are true and which ones false. For typographical convenience we shall use the sign of equality to denote isomorphism.
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