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A Friendly Introduction to Mathematical Logic

A Friendly Introduction to Mathematical Logic

A Friendly Introduction to Mathematical Logic
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ISBN-10:
1942341075
ISBN-13:
9781942341079
Pub. Date:
08/10/2015
Publisher:
Milne Library
ISBN-10:
1942341075
ISBN-13:
9781942341079
Pub. Date:
08/10/2015
Publisher:
Milne Library
A Friendly Introduction to Mathematical Logic

A Friendly Introduction to Mathematical Logic

Overview

At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary's user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition's treatment of languages, structures, and deductions, leading to rigorous proofs of Gödel's First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises.

Product Details

ISBN-13: 9781942341079
Publisher: Milne Library
Publication date: 08/10/2015
Edition description: New Edition
Pages: 380
Sales rank: 995,105
Product dimensions: 6.00(w) x 9.00(h) x 0.85(d)

Table of Contents

1. Structures and Languages.
Naïvely. Languages. Terms and Formulas. Induction. Sentences. Structures. Truth in a Structure. Substitutions and Substitutability. Logical Implication. Summing Up, Looking Ahead.
2. Deductions.
Naïvely. Deductions. The Logical Axioms. Rules of Inference. Soundness. Two Technical Lemmas. Properties of our Deductive System. Non-Logical Axioms. Summing Up, Looking Ahead.
3. Completeness and Compactness.
Naïvely. Completeness. Compactness. The Löwenheim-Skolem Theorems. Summing Up, Looking Ahead.
4. Incompleteness—Groundwork.
Introduction. Language, Structure, Axioms. Recursive Sets, Recursive Functions. Recursive Sets and Computer Programs. Coding—Naïvely. Coding Is Recursive. Gödel Numbering. Gödel Numbers and N. NUM and SUB Are Recursive. Definitions by Recursion Are Recursive. The Collection of Axioms Is Recursive. Coding Deductions. Summing Up, Looking Ahead. Tables of D-Definitions.
5. The Incompleteness Theorems.
Introduction. The Self-Reference Lemma. The First Incompleteness Theorem. Extensions and Refinements. The Second Incompleteness Theorem. Another Explanation of the Second Incompleteness Theorem. Summing Up, Looking Ahead.
Appendix: Set Theory.
Exercises.
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