Branching in the Σ02 -enumeration degrees: a new perspective

We give an alternative and more informative proof that every incomplete \sigmazerotwo-enumeration degree is the meet of two incomparable \sigmazerotwo-degrees, which allows us to show the stronger result that for every incomplete $\Sigma^0_2$-enumeration degree $\degr{a}$, there exist enumeration degrees $\degr{x}_1$ and $\degr{x}_2$ such that $\degr{a}$, $\degr{x}_1$, $\degr{x}_2$ are incomparable, and for all $\degr{b} \leq \degr{a}$, $\degr{b} = \left( \degr{b} \vee \degr{x}_1 \right) \wedge \left( \degr{b} \vee \degr{x}_2 \right)$.