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A Problem Course in Mathematical Logic Version 1. 5 Volume I Propositional and First-Order Logic

By Bilaniuk, Stefan

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Book Id: WPLBN0000661974
Format Type: PDF eBook
File Size: 422.03 KB
Reproduction Date: 2005

Title: A Problem Course in Mathematical Logic Version 1. 5 Volume I Propositional and First-Order Logic  
Author: Bilaniuk, Stefan
Language: English
Subject: Science., Mathematics, Logic
Publication Date:


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Bilaniuk, S. (n.d.). A Problem Course in Mathematical Logic Version 1. 5 Volume I Propositional and First-Order Logic. Retrieved from

Mathematics document containing theorems and formulas.

Excerpt: This book is intended to be the basis for a problem-oriented full-year course in mathematical logic for students with a modicum of mathematical sophistication. Volume I covers the basics of propositional and first-order logic through the Soundness, Completeness, and Compactness Theorems, plus some material on applications of the Compactness Theorem. It could easily be used for a one-semester course on these topics. Volume II covers the basics of computability using Turing machines and recursive functions, the Incompleteness Theorem, and basic complexity theory; it could also be used as for a one-semester course on these topics. In keeping with the modified Moore-method, this book supplies definitions, problems, and statements of results, along with some explanations, examples, and hints. The intent is for the students, individually or in groups, to learn the material by solving the problems and proving the results for themselves. Besides constructive criticism, it will probably be necessary for the instructor to supply further hints or direct the students to other sources from time to time. Just how this text is used will, of course, depend on the instructor and students in question. However, it is probably not appropriate for a conventional lecture-based course nor for a really large class.

Table of Contents
Contents Preface v Introduction 1 Propositional Logic 5 Chapter 1. Language 7 Chapter 2. Truth Assignments 11 Chapter 3. Deductions 15 Chapter 4. Soundness and Completeness 19 First-Order Logic 21 Chapter 5. Languages 23 Chapter 6. Structures and Models 33 Chapter 7. Deductions 41 Chapter 8. Soundness and Completeness 47 Chapter 9. Applications of Compactness 51 Hints 57 Chapter 1. Hints 59 Chapter 2. Hints 61 Chapter 3. Hints 63 Chapter 4. Hints 65 Chapter 5. Hints 67 Chapter 6. Hints 69 Chapter 7. Hints 71


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