Introduction to Mathematical Logic

ISBN-10: 0486497852
ISBN-13: 9780486497853
Edition: 2013
Authors: Richard E. Hodel
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Description: This comprehensive overview of mathematical logic is designed primarily for advanced undergraduates and graduate students of mathematics. The treatment also contains much of interest to advanced students in computer science and philosophy. Topics  More...

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Book details

List price: $40.50
Copyright year: 2013
Publisher: Dover Publications, Incorporated
Publication date: 2/20/2013
Binding: Paperback
Pages: 512
Size: 6.00" wide x 9.00" long x 1.00" tall
Weight: 1.430
Language: English

This comprehensive overview of mathematical logic is designed primarily for advanced undergraduates and graduate students of mathematics. The treatment also contains much of interest to advanced students in computer science and philosophy. Topics include propositional logic; first-order languages and logic; incompleteness, undecidability, and indefinability; recursive functions; computability; and Hilbert's Tenth Problem. 1995 edition.

Preface
Background
Overview of Mathematical Logic
Induction
Formal Systems
Set Theory, Functions, and Relations
Countable and Uncountable Sets
Axiom Systems
Decidability and Computability
Recursive Functions and Recursive Relations
Language and Semantics of Propositional Logic
Language of Propositional Logic
Tautological Consequence
Adequate Sets of Connectives
Propositional Logic
The Formal System P
Soundness Theorem
Deduction Theorem
Model Existence Theorem and Adequacy Theorem
Hilbert-Style Proof Systems for Propositional Logic
Gentzen-Style Proof Systems for Propositional Logic
First-Order Languages
A Language for Arithmetic
First-Order Languages, Interpretations, and Models
Tarski's Definition of Truth
Agreement Theorem and Substitution for Free Variables
First-Order Logic
The Formal System FO<sub>L</sub>
Soundness Theorem
The Deduction Theorem and the Equality Theorem
The Model Existence Theorem
G�del's Completeness Theorems; Decidability and Listability
Replacement Theorem and Prenex Form
Mathematics and Logic
First-Order Theories and Hilbert's Program
The L�wenheim-Skolem Theorem and the Compactness Theorem
Decidable Theories
Zermelo-Frankel Set Theory
Incompleteness, Undecidability, and Indefinability
Overview of the Theorems of Godel, Church, and Tarski
Coding and Expressibility
Recursive Relation &#8594; Expressible Relation
Godel's Incompleteness Theorems
Church's Theorem
Definability and Tarski's Theorem
Recursive Functions
Recursive Functions
Recursive Relations
Recursive Coding Functions
Primitive Recursion
RE Relations
THM<sub>r</sub> Is Not Recursive and TR Is Not Definable
THM<sub>r</sub> Is RE
Computability Theory
Register Machines and RM-Computable Functions
Recursive &#8594; RM-Computable
Kleene Computation Relation T<sub>n</sub>
Partial Recursive Functions
Parameter Theorem and Recursion Theorem
Semi-Thue Systems and Word Problems
Hilbert's Tenth Problem
Overview of Hilbert's Tenth Problem
Diophantine Relations and Functions
RE Relation &#8594; Diophantine Relation (Assuming Bounded &#8704;-Rule
The Exponential Function Is Diophantine
Bounded &#8704;-Rule
Applications of the Main Theorem
Appendix: Number Theory
References and Recommended Readings
Index

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