We prove that the following three conditions are necessary and sufficient for a Boolean algebra A to be embeddable into an interval algebra. (i) A is generated by a subset R such that r s C{0, r, s} for all r, s E R. (ii) A has a complemented subalgebra lattice, where complements can be chosen in a monotone way. (iii) A is isomorphic to ClopX for a compact zero-dimensional topological semilattice (X; ) such that x y z E {fx y, x z} for all x, y, z C X. Boolean algebras that are generated by subchains, i.e. subsets that are linearly ordered under the Boolean partial order, were studied as early as 1939 by A. Mostowski and A. Tarski [9] and have received much attention ever since. Nowadays they are called interval algebras. All basic facts about them can be found in section 15 of [4]. For the sake of brevity we introduce the phrase subinterval algebra to express that a Boolean algebra can be embedded into an interval algebra. Subinterval algebras need not be interval algebras again, the easiest example being the subalgebra generated by an uncountable set of pairwise disjoint elements. Our aim is to give characterizations of subinterval algebras that refer only to the algebra itself. The first of these is in terms of special sets of generators: each subinterval algebra is generated by a ramification set, i.e. a subset R such that r < s or s < r or r s = 0 for all r, s E R. This is equivalent (cf. [5, Theorem 2.3]) to saying that subinterval algebras are what J. D. Monk called pseudo-tree algebras. The other direction being known already (cf. the very nice proof of [5, Theorem 3.1]), it follows that the class of Boolean pseudo-tree algebras coincides with the class of subinterval algebras. As a corollary one gets that the class of pseudo-tree algebras is closed under taking subalgebras. This result answers a question posed by Koppelberg and Monk in [5] and also by van Douwen in [3]. In topological form the characterization was recently proved by S. Purisch [12], who deduced it from a result of J. Nikiel's [10, Theorem 2.1] about the embeddability of certain spaces into dendrons. The author wishes to thank J.D. Monk for making his work-out [8] of Purisch's proof available to him. For superatomic algebras the characterization is also known: in [2] R. Bonnet, M. Rubin and H. Si-Kaddour constructed ramification sets of generators with additional nice properties. Received by the editors November 1, 1995 and, in revised form, March 11, 1996. 1991 Mathematics Subject Classification. Primary 06EO5; Secondary 54F05. (@)1997 American Mathematical Society