2020/08/23 by Cholak, Peter, Downey, Rod, Greenberg, Noam +1
#FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2008.10127
We investigate what collections of c.e. Turing degrees can be realised as the collection of elements of a separating Π01 class of c.e. degree. We show that for every c.e. degree c, the collection \c, 0'\ can be thus realized. We also rule out several attempts at constructing separating classes realizing a unique c.e. degree. For example, we show that there is no super-maximal pair: disjoint c.e. sets A and B whose separating class is infinite, but every separator of c.e. degree is a finite variant of either A or B.