This volume is an independent sequel to the author’s book: Gödel’s incompleteness theorems (1992; Zbl 0787.03003). The book concentrates on those aspects of recursion theory that have application to the metamathematics of incompleteness and undecidability. Not just an advanced textbook, this volume also presents new results in the field. Many of the results presented in the author’s book: Theory of formal systems (1961; Zbl 0097.245) are also presented here in an updated way.
Chapter 0 reviews the previous volume presenting results through Shepherdson’s Theorems. Chapter I discusses recursive enumerability and recursivity. Chapter II treats undecidability and recursive inseparability. Chapter III introduces indexing. Chapter IV discusses generative sets and creative systems. Chapter V continues the discussion with double generativity and complete effective inseparability. Chapter VI treates universal and doubly universal systems. Chapter VII contains an advanced treatment of the Shepherdson Theorem as well as the Putnam- Smullyan Theorem. Chapter VIII covers recursion theorems and Chapter IX continues the discussion with symmetric and double recursion theorems. Chapter X begins the discussion of productivity and double productivity. Chapter XI considers questions in reducibility and the book concludes with Chapter XII on uniform Gödelization. Most of the original material appears in Chapters 6-12.
Intended for experts, the book is tersely but clearly written. A brief list of references points to some of the original presentations of the theorems. This volume will chiefly be useful in advanced graduate courses but will also serve as a standard reference for specialists in the field.