Introduction to Mathematical Logic (Discrete Mathematics and its Applications 6th Revised edition)
By: Elliott Mendelson (author)Hardback
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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 Godel, Church, Kleene, Rosser, and Turing. The sixth edition incorporates recent work on Godel'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 the new edition for historical considerations. The text also offers historical perspectives and many new exercises of varying difficulty, which motivate and lead students to an in-depth, practical understanding of the material.
Elliott Mendelson is professor emeritus at Queens College in Flushing, New York, USA. Dr. Mendelson obtained his bachelor's degree at Columbia University and his master's and doctoral degrees at Cornell University, and was elected afterward to the Harvard Society of Fellows. In addition to his other writings, he is the author of another CRC Press book Introducing Game Theory and Its Applications.
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
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- ID: 9781482237726
6th Revised edition
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