Functional reducts of the countable atomless Boolean algebra

Abstract

For an algebra [Formula: see text] the algebra [Formula: see text] is called a functional reduct if each [Formula: see text] is a term function of [Formula: see text]. 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.