A Nonsplitting Theorem in the Low2 Turing Degrees

The paper proves that for any low2 Δ20-degrees x0 and x1, there exists a low 2-c.e. degree a such that a≠y0∪y1 for all degrees y0⩽x0 and y1⩽x1. It follows that for all m>1 and n=1,2, the posets of lown c.e. and lown m-c.e. degrees are not elementarily equivalent.