遞歸可枚舉集和圖靈度

內(nèi)容概要

　　《國外數(shù)學(xué)名著系列（影印版）31：遞歸可枚舉集和圖靈度：可計(jì)算函數(shù)與》：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。

書籍目錄

IntroductionPart 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 Myhill's 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. Post's Theorem and the Hierarchy Theorem　　3. En-Complete Sets　　4. The Relativized Arithmetical Hierarchy and High and Low DegreesPart B. Post's Problem, Oracle Constructions and the Finite Injury Priority Method　Chapter Ⅴ. Simple Sets and Post's Problem　　1. Immune Sets, Simple Sets and Post's 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. SplittingTheoremsPart 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 LatticeReferencesNotation IndexSubjectIndex

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　　《國外數(shù)學(xué)名著系列（影印版）31：遞歸可枚舉集和圖靈度：可計(jì)算函數(shù)與》為英文影印版。《國外數(shù)學(xué)名著系列（影印版）31：遞歸可枚舉集和圖靈度：可計(jì)算函數(shù)與》是遞歸論方面的主要研究生教材之一，得到了國內(nèi)外同行的廣泛認(rèn)可。

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