Chapter Headings only. Preface. Introduction. VII. Theories of recursive functions. Measures of complexity. Speed of computations. Complexity classes. Time and space measures. Inductive inference. VIII Hierarchies of recursive functions. Small time and space bounds. Deterministic polynomial time. Nondeterministic polynomial time. The polynomial time hierarchy. Polynomial space. Exponential time and space. Elementary functions. Primitive recursive functions. &egr;0-Recursive functions. IX. Recursively enumerable sets. Global properties of recursive sets. Local properties of R.E. sets. Global properties of R.E. sets. Complexity of R.E. sets. Inductive inference of R.E. sets. X. Recursively enumerable degress. The finite injury priority method. Effective Baire category. The infinite injury priority method. The priority method. Many-one degrees. Turing degrees. Comparison of degree theories. Structure inside degrees. Index sets. XI. Limit sets. Jump classes.1-Generic degrees. Structure theory. Minimal degrees. Global properties. Many-one degrees. XII. Arithmetical sets. Forcing in arithmetic. Applications of forcing. Turing degrees of arithmetical sets. XIII. Arithmetical degrees. The theory of arithmetical degrees. An analogue of R.E. sets. An analogue of Post's problem. An analogue of the jump classes. Comparison with R.E. degrees. Enumeration degrees. Enumeration degrees. The theory of enumeration degrees. Enumeration degrees below 0'e. A model of the Lambda calculus. Bibliography. Notation index. Subject index.