Introduction to Mathematical Logic, Fifth Edition
Chapman & Hall/CRC (Verlag)
978-1-58488-876-5 (ISBN)
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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.
Elliott Mendelson is professor emeritus in the Department of Mathematics at Queens College.
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
| Erscheint lt. Verlag | 13.8.2009 |
|---|---|
| Reihe/Serie | Discrete Mathematics and Its Applications |
| Zusatzinfo | very heavy equations, 1000+; 28 Illustrations, black and white |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 856 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre |
| ISBN-10 | 1-58488-876-8 / 1584888768 |
| ISBN-13 | 978-1-58488-876-5 / 9781584888765 |
| Zustand | Neuware |
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