Mendelson Introduction to Mathematical Logic, Fifth Edition

5. Auflage 2011
ISBN: 978-1-58488-877-2
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: 0 - No protection

E-Book, Englisch, 494 Seiten

Reihe: Discrete Mathematics and Its Applications

Retaining all the key features of the previous editions, Introduction to Mathematical Logic, Fifth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. The text also discusses the major results of Gödel, Church, Kleene, Rosser, and Turing.
New to the Fifth Edition

- A new section covering basic ideas and results about nonstandard models of number theory

- A second appendix that introduces modal propositional logic

- An expanded bibliography

- Additional exercises and selected answers

This long-established text continues to expose students to natural proofs and set-theoretic methods. Only requiring some experience in abstract mathematical thinking, it offers enough material for either a one- or two-semester course on mathematical logic.

Zielgruppe

Advanced undergraduate and graduate students in mathematics; computer scientists and electrical engineers.

Autoren/Hrsg.

Mendelson, Elliott

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Mengenlehre
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Algorithmen & Datenstrukturen

Inhaltsverzeichnis

The Propositional Calculus
Propositional Connectives. Truth Tables
Tautologies

Adequate Sets of Connectives

An Axiom System for the Propositional Calculus

Independence. Many-Valued Logics
Other Axiomatizations
First-Order Logic and Model Theory
Quantifiers
First-Order Languages and Their Interpretations. Satisfiability and Truth. Models
First-Order Theories
Properties of First-Order Theories

Additional Metatheorems and Derived Rules

Rule C

Completeness Theorems

First-Order Theories with Equality
Definitions of New Function Letters and Individual Constants

Prenex Normal Forms

Isomorphism of Interpretations. Categoricity of Theories

Generalized First-Order Theories. Completeness and Decidability

Elementary Equivalence. Elementary Extensions
Ultrapowers: Nonstandard Analysis
Semantic Trees

Quantification Theory Allowing Empty Domains
Formal Number Theory

An Axiom System

Number-Theoretic Functions and Relations

Primitive Recursive and Recursive Functions

Arithmetization. Gödel Numbers

The Fixed-Point Theorem. Gödel’s Incompleteness Theorem
Recursive Undecidability. Church’s Theorem
Nonstandard Models
Axiomatic Set Theory
An Axiom System

Ordinal Numbers

Equinumerosity. Finite and Denumerable Sets

Hartogs’ Theorem. Initial Ordinals. Ordinal Arithmetic

The Axiom of Choice. The Axiom of Regularity
Other Axiomatizations of Set Theory
Computability

Algorithms. Turing Machines

Diagrams

Partial Recursive Functions. Unsolvable Problems
The Kleene–Mostowski Hierarchy. Recursively Enumerable Sets

Other Notions of Computability
Decision Problems
Appendix A: Second-Order Logic
Appendix B: First Steps in Modal Propositional Logic
Answers to Selected Exercises
Bibliography
Notation
Index

Über Autor(innen)

Elliott Mendelson is professor emeritus in the Department of Mathematics at Queens College.