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For an algebra = (A , f 1 , ... , f n) the algebra = (A , t 1 , ... , t k) is called a functional reduct if each t j is a term function of . We classify the functional reducts of the countable atomless Boolean algebra up to first-order interdefinability. That is, we consider two functional reducts the "same" if their group of automorphisms is the same. We show that there are 13 such reducts and describe their structures and group of automorphisms. [ABSTRACT FROM AUTHOR]