递归可数集合与度量

Introduction

Part A. The Fundamental Concepts of Recursion Theory

Chapter Ⅰ. Recursive Functions

1. An Informal Description

2. Formal Definitions of Computable Functions

2.1. Primitive Recursive Functions

2.2. Diagonalization and Partial Recursive Functions

2.3. Turing Computable Functions

3. The Basic Results

4. Recursively Enumerable Sets and Unsolvable Problems

5. Recursive Permutations and Myhills Isomorphism Theorem

Chapter Ⅱ. Fundamentals of Recursively Enumerable Sets and the Recursion Theorem

1. Equivalent Definitions of Recursively Enumerable Sets andTheir Basic Properties

2. Uniformity and Indices for Recursive and Finite Sets

3. The Recursion Theorem

4. Complete Sets， Productive Sets， and Creative Sets

Chapter Ⅲ. Turing Reducibility and the Jump Operator

1. Definitions of Relative Computability

2. Turing Degrees and the Jump Operator

3. The Modulus Lemma and Limit Lemma

Chapter Ⅳ. The Arithmetical Hierarchy

1. Computing Levels in the Arithmetical Hierarchy

2. Posts Theorem and the Hierarchy Theorem

3. En-Complete Sets

4. The Relativized Arithmetical Hierarchy and High and Low Degrees

Part B. Posts Problem， Oracle Constructions and the Finite Injury Priority Method

Chapter Ⅴ. Simple Sets and Posts Problem

1. Immune Sets， Simple Sets and Posts Construction

2. Hypersimple Sets and Majorizing Functions

3. The Permitting Method

4. Effectively Simple Sets Are Complete

5. A Completeness Criterion for R.E. Sets

Chapter Ⅵ. Oracle Constructions of Non-R.E. Degrees

1. A Pair of Incomparable Degrees Below 0

2. Avoiding Cones of Degrees

3. Inverting the Jump

4. Upper and Lower Bounds for Degrees

5.* Minimal Degrees

Chapter Ⅶ. The Finite Injury Priority Method

1. Low Simple Sets

2. The Original Friedberg-Muchnik Theorem

3. SplittingTheorems

Part C. Infinitary Methods for Constructing R.E. Sets and Degrees

Chapter Ⅷ.The Infinite Injury Priority Method

1. The Obstacles in Infinite Injury and the Thickness Lemma

2. The Injury and Window Lemmas and the Strong Thickness Lemma

3. TheJump Theorem

4. The Density Theorem and the Sacks Coding Strategy

5.*The Pinball Machine Model for Infinite Injury

Chapter Ⅸ. The Minimal Pair Method and Embedding Lattices into the R.E. Degrees

1. Minimal Pairs and Embedding the Diamond Lattice

2.* Embedding DistributiveLattices

3. The Non-Diamond Theorem

4.* Nonbranching Degrees

5.*Noncappable Degrees

Chapter Ⅹ. The Lattice of R.E. Sets Under Inclusion

……

Part D. Advanced Topics and Current Research Areas in the R.E.Degrees and the Lattice

References

Notation Index

SubjectIndex

《国外数学名著系列（影印版）31：递归可枚举集和图灵度：可计算函数与》：An Informal DescriptionFormal Definitions of Computable FunctionsPrimitive Recursive Functions.Diagonalization and Partial Recursive FunctionsTuring Computable FunctionsThe Basic ResultsRecursive Permutations and Myhills Isomorphism TheoremFundamentals of Recursively Enumerable Sets and the Recursion Theorem。

《国外数学名著系列（影印版）31：递归可枚举集和图灵度：可计算函数与》为英文影印版。《国外数学名著系列（影印版）31：递归可枚举集和图灵度：可计算函数与》是递归论方面的主要研究生教材之一，得到了国内外同行的广泛认可。