Introduction to Mathematical Logic, Sixth Edition

✍ Scribed by Mendelson, Elliott

• Publisher: CRC Press
• Year: 2015
• Tongue: English
• Leaves: 499
• Series: Discrete Mathematics and Its Applications
• Edition: 6th ed
• Category: Library

✦ Synopsis

The new edition of this classic textbook, Introduction to Mathematical Logic, Sixth 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.The sixth edition incorporates recent work on Gödel's second incompleteness theorem as well as restoring an appendix on consistency proofs for first-order arithmetic. This appendix last appeared in the first edition. It is offered in th... Read more...

Abstract:

Explores the principal topics of mathematical logic. This title covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. It discusses the major results of Godel, Church, Kleene, Rosser, and Turing. Read more...

✦ Table of Contents

Content: Preface Introduction 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: Godel Numbers The Fixed-Point Theorem: Godel'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 Appendix C: A Consistency Proof for Formal Number Theory Answers to Selected Exercises Bibliography Notations Index

✦ Subjects

Математика;Математическая логика;