Classical Recursion Theory —— The Theory of Functions and Sets of Natural Numbers

----- 古典递归理论：函数和自然数集理论

ISBN: 9780444872951 出版年：1992 页码：689 Odifreddi, P North Holland_RM

Recursiveness and Computability. Induction. Systems of Equations. Arithmetical Formal Systems. Turing Machines. Flowcharts. Functions as Rules. Arithmetization. Church's Thesis. Basic Recursion Theory. Partial Recursive Functions. Diagonalization. Partial Recursive Functionals. Effective Operations. Indices and Enumerations. Retraceable and Regressive Sets. Post's Problem and Strong Reducibilities. Post's Problem. Simple Sets and Many-One Degrees. Hypersimple Sets and Truth-Table Degrees. Hyperhypersimple Sets and Q-Degrees. A Solution to Post's Problem. Creative Sets and Completeness. Recursive Isomorphism Types. Variations of Truth-Table Reducibility. The World of Complete Sets. Formal Systems and R.E. Sets. Hierarchies and Weak Reducibilities. The Arithmetical Hierarchy. The Analytical Hierarchy. The Set-Theoretical Hierarchy. The Constructible Hierarchy. Turing Degrees. The Language of Degree Theory. The Finite Extension Method. Baire Category. The Coinfinite Extension Method. The Tree Method. Initial Segments. Global Properties. Degree Theory with Jump. Many-One and Other Degrees. Distributivity. Countable Initial Segments. Uncountable Initial Segments. Global Properties. Comparison of Degree Theories. Structure Inside Degrees. Bibliography. Index.