A Problem Course
in
Mathematical Logic

... is a freeware mathematics text by Stefan Bilaniuk.

Current Release: Version 1.6

Released under the GNU Free Documentation License, Version 1.2 or later.


Description | Availability | Conditions | History | Contacting the author

Description

A Problem Course in Mathematical Logic is intended to serve as the text for an introduction to mathematical logic for undergraduates with some mathematical sophistication. It supplies definitions, statements of results, and problems, along with some explanations, examples, and hints. The idea is for the students, individually or in groups, to learn the material by solving the problems and proving the results for themselves. The book should do as the text for a course taught using the modified Moore-method.

The material and its presentation are pretty stripped-down and it will probably be desirable for the instructor to supply further hints from time to time or to let the students consult other sources. Various concepts and and topics that are often covered in introductory mathematical logic or computability courses are given very short shrift or omitted entirely, among them normal forms, definability, and model theory.

Parts I and II, Propositional Logic and First-Order Logic respectively, cover the basics of these topics through the Soundness, Completeness, and Compactness Theorems, plus a little on applications of the Compactness Theorem. They could be used for a one-term course on these subjects. Part III, Computability, covers the basics of computability using Turing machines and recursive functions; it could be used as the basis of a one-term course. Part IV, Incompleteness, is concerned with proving the Gödel Incompleteness Theorems. With the omission of some topics from Part III which are not needed to prove the results in Part IV, Parts III and IV could be used for a one-term course for students who know the contents of Part II already.


Availability

A Problem Course in Mathematical Logic is available via http in LaTeX, PDF, and PostScript formats. Unless you have unusual constraints or requirements, or wish to modify the text, you should probably get the PDF format. If you have any problems downloading or printing these files, please contact the author.


Conditions

A Problem Course in Mathematical Logic, Version 1.6, is Copyright (c) 1994-2003 by Stefan Bilaniuk. Permission is granted to copy, distribute and/or modify this document 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 text, in Appendix D, GNU Free Documentation License.)

The gist is that you are free to copy, distribute, and use A Problem Course in Mathematical Logic, Version 1.6, unchanged, but there are some restrictions on what you can do if you wish to make changes. If you wish to use this text in a manner not covered by the GNU Free Documentation License, please contact the author.


Revision history

Version 1.6

Version 1.5

Version 1.4

Version 1.3

Version 1.2

Version 1.1

Version 1.0


Contacting the author

If you have questions, comments, corrections, suggestions, or requests, please contact the author at one of the following:

Stefan Bilaniuk
Department of Mathematics
Trent University
Peterborough, Ontario
Canada K9J 7B8

telephone: 705 748-1011x1474 (office) or 705 755-1193 (home)
e-mail: sbilaniuk@trentu.ca


Stefan Bilaniuk
Department of Mathematics
Trent University
Maintained by Stefan Bilaniuk. Last updated 2003.09.02.