Splitting Properties of Total Enumeration Degrees
We describe general conditions under which relative splittings and specified diamond embeddings are derivable in the local structure of enumeration degrees (e-degrees). In so doing, we touch upon three basic issues: the possibility for studying properties of Turing degrees via enumeration reducibility; general definability problems and the role of splitting and non-splitting; and (emerging from the techniques developed) the description of new relationships between information content and degree theoretic structure.