- 数学家用的数理逻辑教程(第2版影印版)(英文版)
- - 作者：(德)Y.I.马宁
  - 出版社：世界图书出版公司
  - ISBN：9787519255336
  - 出版日期：2019/03/01
  - 页数：384
- 售价：47.6

内容大纲
《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。
作者介绍
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
    1  Unique Reading Lemma
    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
    4  Operads and PROPs
    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

Suggestions for Further Reading
Index

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