数学家用的数理逻辑教程(第2版影印版)(英文版)

• 定价： ￥119
• ISBN：9787519255336
• 开 本：16开 平装
• 作者：(德)Y.I.马宁
• 立即节省：
• 2019-03-01 第1版
• 2019-03-01 第1次印刷

内容提要

《数学家用的数理逻辑教程(第2版影印版)(英文版)》作者Y.I.马宁是前苏联杰出的数学家，从事数论与代数几何研究工作。本书分为四大部分进行论述，是一部不可多得的数理逻辑教材，可作为高校数学专业研究生教材，及相关专业数学工作者参考书。

目录

Preface to the Second Edition
Preface to the First Edition
Ⅰ  PROVABILITY
Ⅰ  Introduction to Formal Languages
1  General Information
2  First-Order Languages
Digression: Names
3  Beginners' Course in Translation
Digression: Syntax
Ⅱ  Truth and Deducibility
2  Interpretation: Truth, Definability
3  Syntactic Properties of Truth
Digression: Natural Logic
4  Deducibility
Digression: Proof
5  Tautologies and Boolean Algebras
Digression: Kennings
6  Godel's Completeness Theorem
7  Countable Models and Skolem's Paradox
8  Language Extensions
9  Undefinability of Truth: The Language SELF
10  Smullyan's Language of Arithmetic
11  Undefinability of Truth: Tarski's Theorem
Digression: Self-Reference
12  Quantum Logic
Appendix: The Von Neumann Universe
The Last Digression. Truth as Value and Duty: Lessons of Mathematics
Ⅲ  The Continuum Problem and Forcing
1  The Problem: Results, Ideas
2  A Language of Real Analysis
3  The Continuum Hypothesis Is Not Deducible in L2 Real
4  Boolean-Valued Universes
5  The Axiom of Extensionality Is "True"
6  The Axioms of Pairing, Union, Power Set, and Regularity Are "True"
7  The Axioms of Infinity, Replacement, and Choice Are "True".
8  The Continuum Hypothesis Is "False" for Suitable B
9  Forcing
Ⅳ  The Continuum Problem and Constructible Sets
1  Godel's Constructible Universe
2  Definability and Absoluteness
3  The Constructible Universe as a Model for Set Theory
4  The Generalized Continuum Hypothesis Is L-True
5  Constructibility Formula
6  Remarks on Formalization
7  What Is the Cardinality of the Continuum?
Ⅱ  COMPUTABILITY
Ⅴ  Recursive Functions and Church's Thesis
1  Introduction. Intuitive Computability
2  Partial Recursive Functions
3  Basic Examples of Recursiveness
4  Enumerable and Decidable Sets
5  Elements of Recursive Geometry
Ⅵ  Diophantine Sets and Algorithmic Undecidability
1  The Basic Result
2  Plan of Proof
3  Enumerable Sets Are D-Sets
4  The Reduction
5  Construction of a Special Diophantine Set
6  The Graph of the Exponential Is Diophantine
7  The Factorial and Binomial Coefficient Graphs Are Diophantine
8  Versal Families
9  Kolmogorov Complexity
Ⅲ  PROVABILITY AND COMPUTABILITY
Ⅶ  Godel's Incompleteness Theorem
1  Arithmetic of Syntax
2  Incompleteness Principles
3  Nonenumerability of True Formulas
4  Syntactic Analysis
5  Enumerability of Deducible Formulas
6  The Arithmetical Hierarchy
7  Productivity of Arithmetical Truth
8  On the Length of Proofs
Ⅷ  Recursive Groups
1  Basic Result and Its Corollaries
2  Free Products and HNN-Extensions
3  Embeddings in Groups with Two Generators
4  Benign Subgroups
5  Bounded Systems of Generators
6  End of the Proof
Ⅸ  Constructive Universe and Computation
1  Introduction: A Categorical View of Computation
2  Expanding Constructive Universe: Generalities
3  Expanding Constructive Universe: Morphisms
5  The World of Graphs as a Topological Language
6  Models of Computation and Complexity
7  Basics of Quantum Computation I: Quantum Entanglement
8  Selected Quantum Subroutines
9  Shot's Factoring Algorithm
10  Kolmogorov Complexity and Growth of Recursive Functions
Ⅳ  MODEL THEORY
Ⅹ  Model Theory
1  Languages and Structures
2  The Compactness Theorem
3  Basic Methods and Constructions
4  Completeness and Quantifier Elimination in Some Theories
5  Classification Theory
6  Geometric Stability Theory
7  Other Languages and Nonelementary Model Theory