Density of Recursively Inseparable R. E. Sets and Universal Recrusively Inseparability

Problems about density are remarkable in the theory of degrees of unsolvability. Owing to their difficulty few results have been obtained till now. Sacks 1964 showed that the r. e. degrees are dense; Fejer 1980 showed that nonbraching degrees are dense in the r.e. degrees, this is the first nontrivial definable subset of the degrees known to be dense.