The discontinuity of splitting in the recursively enumerable degrees

In this paper we examine a class of pairs of recursively enumerable degrees, which is related to the Slaman-Soare Phenomenon.Preparation of this paper supported by S.E.R.C. (UK) Research Grant no. GR/H 02165, and by European network Complexity, Logic and Recursion Theory (EC Contract No. ERBCHRXCT930415). The second author wishes to thank Alistair H. Lachlan and the University of Leeds