This volume is a collection of refereed research articles commemorating the Leeds Recursion Theory Year 1993-94. The year was funded principally by the (then) UK Science and Engineering Research Council, with additional support from the London Mathematical Society, European Twinning/Human Capital and Mobility Networks on ‘Complexity, Logic and Recursion Theory’, and on ‘Proof Theory and Computation’, a MURST-British Council travel grant, an EC PECO visiting fellowship, and with the backing of the Leeds University Department of Pure Mathematics. We thank them all for enabling an invigorating year.

It is fifteen years since the publication of the last Leeds Recursion Theory volume in this same series (LMS Lecture Notes 45). In that time the subject has made great strides. New methods have been developed and out of the immense technical machinery have finally emerged solutions to long-standing problems which originally motivated the pioneers some forty years ago, notably on definability, decidability and automorphisms for recursion theoretic structures. In addition the fundamental ideas concerning computation and recursion have naturally found their place at the interface between logic and theoretical computer science, and the feedback continues to motivate mathematical research in a variety of new directions. Thus the following contributions provide a picture of current ideas and methods in the ongoing investigations of the structure of the computable and non-computable universe. A number of the articles contain introductory and background material, which it is hoped will make the volume an invaluable source of information for specialist and non-specialist alike.