國外數學名著係列（影印版）31：遞歸可枚舉集和圖靈度 可計算函數與可計算生成集研究 [Recursively Enumerable Sets and Degrees:A Study of Comput pdf epub mobi txt 電子書 下載 2025

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Robert，I.Soare 著

齣版社： 科學齣版社

ISBN：9787030182951

版次：1

商品編碼：11918288

包裝：精裝

叢書名： 國外數學名著係列（影印版）

外文名稱：Recursively Enumerable Sets and Degrees:A Study of Computable Functions and Computably Generated Sets##

內容簡介

　　《國外數學名著係列（影印版）31：遞歸可枚舉集和圖靈度 可計算函數與可計算生成集研究》主要內容包括：An Informal DescriptionFormal Definitions of Computable FunctionsPrimitive Recursive Functions.Diagonalization and Partial Recursive FunctionsTuring Computable FunctionsThe Basic ResultsRecursive Permutations and Myhill's Isomorphism TheoremFundamentals of Recursively Enumerable Sets and the Recursion Theorem。

內頁插圖

目錄

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 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 Degrees

Part 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． 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
Subject Index

前言/序言

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