pcml-16 - A Problem Course in Mathematical Logic Version...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
A Problem Course in Mathematical Logic Version 1.6 Stefan Bilaniuk Department of Mathematics Trent University Peterborough, Ontario Canada K9J 7B8 E-mail address : sbilaniuk@trentu.ca
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
1991 Mathematics Subject Classification. 03 Key words and phrases. logic, computability, incompleteness Abstract. This is a text for a problem-oriented course on math- ematical logic and computability. Copyright c ± 1994-2003 Stefan Bilaniuk. Permission is granted to copy, distribute and/or modify this doc- ument under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the sec- tion entitled “GNU Free Documentation License”. This work was typeset with L A T E X, using the A M S -L A T E Xand A M S Fonts packages of the American Mathematical Society.
Background image of page 2
Contents Preface v Introduction ix Part I. Propositional Logic 1 Chapter 1. Language 3 Chapter 2. Truth Assignments 7 Chapter 3. Deductions 11 Chapter 4. Soundness and Completeness 15 Hints for Chapters 1–4 17 Part II. 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 53 Hints for Chapters 5–9 59 Part III. Computability 65 Chapter 10. Turing Machines 67 Chapter 11. Variations and Simulations 75 Chapter 12. Computable and Non-Computable Functions 81 Chapter 13. Recursive Functions 87 Chapter 14. Characterizing Computability 95 iii
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
iv CONTENTS Hints for Chapters 10–14 101 Part IV. Incompleteness 109 Chapter 15. Preliminaries 111 Chapter 16. Coding First-Order Logic 113 Chapter 17. Defining Recursive Functions In Arithmetic 117 Chapter 18. The Incompleteness Theorem 123 Hints for Chapters 15–18 127 Appendices 131 Appendix A. A Little Set Theory 133 Appendix B. The Greek Alphabet 135 Appendix C. Logic Limericks 137 Appendix D. GNU Free Documentation License 139 Appendix. Bibliography 147 Appendix. Index 149
Background image of page 4
Preface This book is a free text intended to be the basis for a problem- oriented course(s) in mathematical logic and computability for students with some degree of mathematical sophistication. Parts I and II cover the basics of propositional and first-order logic respectively, Part III covers the basics of computability using Turing machines and recursive functions, and Part IV covers G¨ odel’s Incompleteness Theorems. They can be used in various ways for courses of various lengths and mixes of material. The author typically uses Parts I and II for a one-term course on mathematical logic, Part III for a one-term course on computability, and/or much of Part III together with Part IV for a one-term course on computability and incompleteness.
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 06/13/2009 for the course TAM 455 taught by Professor Petrina during the Fall '08 term at Cornell University (Engineering School).

Page1 / 166

pcml-16 - A Problem Course in Mathematical Logic Version...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online