SOME FUNDAMENTAL ISSUES CONCERNING DEGREES OF UNSOLVABILITY
Stephen G. Simpson · Lecture notes series, Institute For Mathematical Sciences · 2008
Recall that RT is the upper semilattice of recursively enumerable Turing degrees. We consider two fundamental, classical, unresolved issues concerning RT. The first issue is to find a specific, natural, recursively enumerable Turing degree a ∈ RT which is> 0 and 0 and < 0 ′. In order to address these issues, we embed RT into a slightly larger degree structure, Pw, which is much better behaved. Namely, Pw is the lattice of weak degrees of mass problems associated with nonempty Π 0 1 subsets of 2 ω. We define a specific, natural embedding of RT into Pw, and we present some recent and new research results.