There is no low maximal d. c. e. degree

Abstract

We show that for any computably enumerable (c. e.) set A and any Δ0 2 set L, if L is low and L <T A, then there is a c. e. splitting A0 ∐ A1 = A such that Ai ⊗ L <T A. In particular, if L is low and n-c. e., then Ai ⊗ L is n-c. e. and hence there is no low maximal n-c. e. degree.