Strong reducibilities

Abstract

Acknowledgements 1. Introduction 2. Where it all started: Post's problem and ^-completeness 3. The structure inside single degrees 4. The structure of m-degrees 5. The structure of 1-degrees 6. The structure of //-degrees 7. Elementary equivalence and undecidability 8. Where we end: variations on the theme of ^-reductibility Acknowledgements. During the writing of the first draft I have been helped in many ways by Carl Jockusch, Jr., who patiently explained to me an incredible number of results on these and other topics.