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We give some general theorems on free algebras of varieties of Booleanalgebras with operators; a hitherto new result is obtained for Pinter'ssubstitution algebras. For n\geq 3, and m>1, there is a generating set of thefree algebra freely generated by m elements, which is not a free set ofgenerators.

On atomicity of free algebras in Boolean algebras with operators, and a new result on Pinter's free algebras