Introduction to Mathematical Logic
1st Edition
Published on 1. June 1997
Book
Hardback
440 pages
978-0-412-80830-2 (ISBN)
Description
The Fourth Edition of this long-established text retains all the key features of the previous editions, covering the basic topics of a solid first course in mathematical logic. This edition includes an extensive appendix on second-order logic, a section on set theory with urlements, and a section on the logic that results when we allow models with empty domains. The text contains numerous exercises and an appendix furnishes answers to many of them.
Introduction to Mathematical Logic includes:
propositional logic
first-order logic
first-order number theory and the incompleteness and undecidability theorems of Goedel, Rosser, Church, and Tarski
axiomatic set theory
theory of computability
The study of mathematical logic, axiomatic set theory, and computability theory provides an understanding of the fundamental assumptions and proof techniques that form basis of mathematics. Logic and computability theory have also become indispensable tools in theoretical computer science, including artificial intelligence. Introduction to Mathematical Logic covers these topics in a clear, reader-friendly style that will be valued by anyone working in computer science as well as lecturers and researchers in mathematics, philosophy, and related fields.
Introduction to Mathematical Logic includes:
propositional logic
first-order logic
first-order number theory and the incompleteness and undecidability theorems of Goedel, Rosser, Church, and Tarski
axiomatic set theory
theory of computability
The study of mathematical logic, axiomatic set theory, and computability theory provides an understanding of the fundamental assumptions and proof techniques that form basis of mathematics. Logic and computability theory have also become indispensable tools in theoretical computer science, including artificial intelligence. Introduction to Mathematical Logic covers these topics in a clear, reader-friendly style that will be valued by anyone working in computer science as well as lecturers and researchers in mathematics, philosophy, and related fields.
More details
Series
Edition
1., 997
Language
English
Place of publication
London
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
College/higher education
Professional and scholarly
Research
Edition type
New edition
Dimensions
Height: 235 mm
Width: 156 mm
Weight
710 gr
ISBN-13
978-0-412-80830-2 (9780412808302)
Schweitzer Classification
Other editions
New editions
Elliott Mendelson
Introduction to Mathematical Logic, Fifth Edition
Book
08/2009
5th Edition
Chapman & Hall/CRC
€81.89
Article exhausted; check different version
Previous edition
Elliot Mendelson
Introduction to Mathematical Logic
Book
03/1987
1st Edition
CRC Press
€144.99
Article exhausted; check for reprint
Content
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
Quantification Theory
Quantifiers
First-Order Languages and Their Interpretations
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. Non-Standard Analysis
Semantic Trees
Quantification Theory Allowing Empty Domains
Formal Number Theory
An Axiom System
Number-Theoretic Functions and Relations
Primitive Recursive and Recursive Functions
Arithmatization. Goedel Numbers
The Fixed Point Theorem. Goedel's Incompleteness Theorem
Recursive Undecidability. Church's Theorem
Axiomatic Set Theory
An Axiom System
Ordinal Numbers
Equinumerousity. Finite and Denumerable Sets.
Hartog's 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-Mosotovski Hierarchy. Recursively Enumerable Sets
Other notions of Computability
Decision Problems
Propositional Connectives. Truth Tables
Tautologies
Adequate Sets of Connectives
An Axiom System for the Propositional Calculus
Independence: Many-Valued Logics
Other Axiomatizations
Quantification Theory
Quantifiers
First-Order Languages and Their Interpretations
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. Non-Standard Analysis
Semantic Trees
Quantification Theory Allowing Empty Domains
Formal Number Theory
An Axiom System
Number-Theoretic Functions and Relations
Primitive Recursive and Recursive Functions
Arithmatization. Goedel Numbers
The Fixed Point Theorem. Goedel's Incompleteness Theorem
Recursive Undecidability. Church's Theorem
Axiomatic Set Theory
An Axiom System
Ordinal Numbers
Equinumerousity. Finite and Denumerable Sets.
Hartog's 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-Mosotovski Hierarchy. Recursively Enumerable Sets
Other notions of Computability
Decision Problems