A Problem Course
in
Mathematical Logic

Description

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

• LaTeX source [~340K]
  LaTeX, with the AmS-LaTeX and AmSFonts packages, is needed to typeset this file.

• Portable Document Format (PDF) [~730K]

• PostScript (compressed zip file) [~1100K]

Conditions

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

• Minor additions and revisions.
• 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