Sets of generator and automorphism bases for the enumeration degrees (Q1295393)

A set \(A\) is enumeration reducible to a set \(B\) \((A\leq_e B)\) if there exists an effective procedure for enumerating \(A\) starting from any enumeration of \(B\). The degree structure \({\mathfrak D}_e\) originated by \(\leq_e\) is the structure of the enumeration degrees. Similar to the case of Turing degrees, there is a wide-spread discussion about the structural and global properties of \({\mathfrak D}_e\). This paper shows some interesting properties about automorphisms of enumeration degrees and exhibits several automorphism bases for \({\mathfrak D}_e\).