Introduction. Let S!I be a countable atomless Boolean algebra and let X be a countable partial ordering. We prove that there exists an embedding of X intod which is recursive in X, S!I and which destroys all suprema and infima of X which can be destroyed. We show that the above theorem is false when we try to preserve all suprema and infima of X instead of destroying them. Finally we indicate that if d and f!fi are countable Boolean algebras and f!J is atomless thend can be embedded into f!J by

more »

... a function which is recursive in ef, f!J. If d is also atomless, then there is an isomorphism from d into f!J which is recursive ind, f!J. 1. Preliminaries. Throughout the paper w denotes the set of natural numbers, and cf> the empty set. If X is a set and n a natural number then xn denotes the set of all n-tuples of elements of X. We say that X is a partial ordering on a set A (p.a. on A) if for some B C A X C B 2 and for all x, y, z E B .