Functional reducts of the countable atomless Boolean algebra

For an algebra 2l = (A, f(1), ... f(n)) the algebra B = (A, t(1), ..., t(k)) is called a functional reduct if each tj is a term function of 2l. 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.