# 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

• The two volumes combined into one.
• Released 2003.09.02. [Sorry for the very long delay...]
• Minor revisions and corrections to Parts I (propositional logic) and II (first-order-logic), the two parts of the old Volume I.
• Substantial revisions and corrections to Part III (computability) and lesser revisions and corrections to Part IV (incompleteness), the two parts of the old Volume II.

### Version 1.5

• Corrections and minor revisions to Volume I.
• Volume I released: 1999.09.13.
• Volume II release anticipated in January 1999. [Didn't happen. Sigh.]
• Expiry date: 2000.12.31.

### Version 1.4

• Corrections and minor revisions to Volume I.
• Considerable revisions to Volume II, left unfinished.
• Limited release in pieces over the 1998-1999 school year.
• Expiry date: 1999.12.31.

### Version 1.3

• Corrected all known typos and other errors.
• Released 1997.08.23.
• Expiry date: 1998.12.31. Extended to 2000.12.31

### Version 1.2

• Revisions to material on incompleteness (Chapters 16-19)
• Major revisions to material on computability (Chapters 10-15).
• Major revisions to material on applications of Compactness (Chapter 9).
• Minor additions and revisions throughout.
• Corrected all known typos and other errors.
• Added a proper index to Volume II.
• Released 1996.02.29. (First publicised release.)
• Expiry date: 1997.12.31.

### Version 1.1

• Added Volume II, Computability and Incompleteness (rudimentary index only).
• Updated for LaTeX2e with the AmS-LaTeX 1.2 and AmSFonts 2.1 packages.
• Corrected a few typos and other errors.
• Released 1995.12.07.
• Expiry date: 1996.12.31.

### Version 1.0

• Included Volume I, Propositional and First-Order Logic, only.
• Used AmS-LaTeX 1.1 with AmSFonts 2.1.
• Released 1994.09.11. (First public release.)
• Expiry date: 1996.12.31.

## Contacting the author

Stefan Bilaniuk
Department of Mathematics
Trent University
Peterborough, Ontario
e-mail: `sbilaniuk@trentu.ca`