Recursion-Theoretic Hierarchies Perspectives in Logic Series

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. The theory set out in this volume, the ninth publication in the Perspectives in Logic series, is the result of the meeting and common development of two currents of mathematical research: descriptive set theory and recursion theory. Both are concerned with notions of definability and with the classification of mathematical objects according to their complexity. These are the common themes which run through the topics discussed here. The author develops a general theory from which the results of both areas can be derived, making these common threads clear.

Introduction; Part I. Basic Notations of Definability: 1. Groundwork; 2. Ordinary recursion theory; 3. Hierarchies and definability; Part II. The Analytical and Projective Hierarchies: 4. The first level; 5. Δ^1_2 and beyond; Part III. Generalized Recursion Theories: 6. Recursion in a type-2 functional; 7. Recursion in a type-3 functional; 8. Recursion on ordinals; Epilogue; References; Global notational conventions; Special notations; Index.

Peter G. Hinman works in the Department of Mathematics at the University of Michigan, Ann Arbor.