The structure of countable Boolean algebras


A structure theory for denumerable Boolean algebras is presented. The isomorphism types of countable Boolean algebras are completely characterized in terms of certain naturally defined invariants. As an application, we show that any countable commutative semigroup can be embedded into the semigroup of the isomorphism types of all countable Boolean algebras under direct product. This solves in paritcular the cube problem of Tarski.


Jussi Ketonen