Table of Contents

Honest polynomial reductions and exptally sets.- On the structure of degrees below O?.- Positive solutions to Post's problem.- The metamathematics of Fraïssé's order type conjecture.- Enumeration reducibility, nondeterministic computations and relative computability of partial functions.- Notes on the O? priority method with special attention to density results.- Array nonrecursive sets and multiple permitting arguments.- Superbranching degrees.- A direct construction of a minimal recursively enumerable truth-table degree.- ?2-induction and the construction of a high degree.- Undecidability and initial segments of the wtt-degrees ?0?.- Randomness and generalizations of fixed point free functions.- Recursive enumeration without repetition revisited.- Priority arguments using iterated trees of strategies.- On the relationship between the complexity, the degree, and the extension of a computable set.- Polynomially isolated sets.- A characterization of effective topological spaces.

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