A tour through mathematical logic /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Wolf, Robert S.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Washington, D.C. : Mathematical Association of America, ©2005.
Colección:Carus mathematical monographs ; no. 30.
Temas:
Logic, Symbolic and mathematical.
Algebra, Abstract.
Logique symbolique et mathématique.
Algèbre abstraite.
MATHEMATICS > Logic.
Algebra, Abstract
Logic, Symbolic and mathematical
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • copyright page
  • title page
  • Preface
  • Contents
  • 1 Predicate Logic
  • 1.1 Introduction
  • A very brief history of mathematical logic
  • Short Bio: Bertrand Russell
  • 1.2 Propositional logic
  • 1.3 Quantifiers
  • Uniqueness
  • Proof methods based on quantifiers
  • Translating statements into symbolic form
  • 1.4 First-order languages and theories
  • Short Bio: Euclid
  • 1.5 Examples of first-order theories
  • 1.6 Normal forms and complexity
  • Second-order logic and Skolem form
  • 1.7 Other logics
  • Many-valued logic
  • Fuzzy logic
  • Modal logic
  • Nonmonotonic logic.
  • Temporal logic
  • 2 Axiomatic Set Theory
  • 2.1 Introduction
  • 2.2 "Naive" set theory
  • Short Bio: Georg Ferdinand Cantor
  • 2.3 Zermelo-Fraenkel set theory
  • Proper axioms of ZF set theory
  • Short bio: John von Neumann
  • The regularity axiom
  • 2.4 Ordinals
  • 2.5 Cardinals and the cumulative hierarchy
  • Von Neumann cardinals
  • The cumulative hierarchy
  • 3 Recursion Theory and Computability
  • 3.1 Introduction
  • Short Bio: Emil Post
  • 3.2 Primitive recursive functions
  • 3.3 Turing machines and recursive functions
  • Short Bio: Alan Turing
  • The mu operator.
  • 3.4 Undecidability and recursive enumerability
  • Recursive enumerability
  • 3.5 Complexity theory
  • Nondeterministic Turing machines, and P vs. NP
  • 4 Gödel's Incompleteness Theorems
  • 4.1 Introduction
  • 4.2 The arithmetization of formal theories
  • Short Bio: Kurt Gödel
  • The recursion theorem
  • 4.3 A potpourri of incompleteness theorems
  • An historical perspective on Gödel's work
  • Gödel's second incompleteness theorem
  • Hilbert's formalist program, revisited
  • 4.4 Strengths and limitations of PA
  • Ramsey's theorems and the Paris-Harrington results
  • Short Bio: Frank Ramsey.
  • 5 Model Theory
  • 5.1 Introduction
  • 5.2 Basic concepts of model theory
  • 5.3 The main theorems of model theory
  • The Löwenheim-Skolem
  • Tarski theorem
  • 5.4 Preservation theorems
  • Preservation under submodels and intersections
  • Preservation under unions of chains
  • Preservation under homomorphic images
  • Preservation under direct products
  • 5.5 Saturation and complete theories
  • Short Bio: Julia Robinson
  • 5.6 Quantifier elimination
  • 5.7 Additional topics in model theory
  • Axiomatizable and nonaxiomatizable classes
  • Stone spaces
  • Tarski's undefinability theorem.
  • Second-order model theory
  • 6 Contemporary Set Theory
  • 6.1 Introduction
  • Some more history of set theory
  • 6.2 The relative consistency of AC and GCH
  • 6.3 Forcing and the independence results
  • 6.4 Modern set theory and large cardinals
  • Large cardinals and the consistency of ZF
  • 6.5 Descriptive set theory
  • Classical descriptive set theory
  • Short Bio: Nikolai Luzin
  • 6.6 The axiom of determinacy
  • Infinite games
  • Woodin's program
  • 7 Nonstandard Analysis
  • 7.1 Introduction
  • "Limits vs. infinitesimals" through the ages
  • Short Bio: Archimedes.

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