Table of contents : Honest polynomial reductions and exptally sets....Pages 1-22 On the structure of degrees below O′....Pages 23-32 Positive solutions to Post's problem....Pages 33-40 The metamathematics of Fraïssé's order type conjecture....Pages 41-56 Enumeration reducibility, nondeterministic computations and relative computability of partial functions....Pages 57-110 Notes on the O‴ priority method with special attention to density results....Pages 111-140 Array nonrecursive sets and multiple permitting arguments....Pages 141-173 Superbranching degrees....Pages 175-186 A direct construction of a minimal recursively enumerable truth-table degree....Pages 187-204 Σ 2 -induction and the construction of a high degree....Pages 205-221 Undecidability and initial segments of the wtt-degrees ≤0′....Pages 223-244 Randomness and generalizations of fixed point free functions....Pages 245-254 Recursive enumeration without repetition revisited....Pages 255-275 Priority arguments using iterated trees of strategies....Pages 277-296 On the relationship between the complexity, the degree, and the extension of a computable set....Pages 297-322 Polynomially isolated sets....Pages 323-362 A characterization of effective topological spaces....Pages 363-387