Editing Many-one reduction (section)

== Many-one reductions extended ==
One may also ask about generalized cases of many-one reduction. One such example is ''e-reduction'', where we consider <math>f:A\to B</math> that are recursively enumerable instead of restricting to recursive <math>f</math>. The resulting reducibility relation is denoted <math>\leq_e</math>, and its poset has been studied in a similar vein to that of the Turing degrees. For example, there is a jump set <math>\boldsymbol 0^'_e</math> for ''e''-degrees. The ''e''-degrees do admit some properties differing from those of the poset of Turing degrees, e.g. an embedding of the diamond graph into the degrees below <math>\boldsymbol'_e</math>.<ref>S. Ahmad, [https://www.jstor.org/stable/2274914 Embedding the Diamond in the <math>\Sigma_2</math> Enumeration Degrees] (1991). [[Journal of Symbolic Logic]], vol.56.</ref>