An atomless interval Boolean algebra A such that $ mathfrak{a} (A) $ < $ mathfrak{t} (A) $

For any Boolean algebra A, is the smallest cardinality of an infinite partition of unity in A. A tower in a Boolean algebra A is a subset X of A well-ordered by the Boolean ordering, with but with is the smallest cardinality of a tower of A. Given a linearly ordered set L with first element, the interval algebra of L is the algebra of subsets of L generated by the half-open intervals [a, b). We prove that there is an atomless interval algebra A such that . Received January 21, 2002; accepted in final form March 13, 2002.