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It is shown that for any computably enumerable (c.e.) degree w, if w6= 0, then there is a c.e. degree a such that (a_ w)0 = a00 = 000 (so a is low2 and a_ w is high). It follows from this and previous work of P. Cholak, M. Groszek and T. Slaman that the low and low2 c.e. degrees are not elementarily equivalent as partial orderings.

A join theorem for the computably enumerable degrees