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Introduction to Logic MAT 6973 Fall, 2004 Instructor: J. Iovino |
The course has been scheduled for Tuesday, Thursday, 3:30pm-4:45pm.
Prerequisites
Real Analysis I (MAT 4213) or consent of instructor.Content
The course is an introduction to the basic concepts of mathematical logic, and is divided in three parts.- Part 1: First Order Logic.
- First order logic, proof systems.
- Part 2: Completeness.
- The Completeness Theorem, the Compactness Theorem, nonstandard models of arithmetic.
- Part 3: Incompleteness and Undecidability.
- Peano Arithmetic, Gödel numbers, recursive sets and functions, Gödel's Incompleteness Theorem, undecidability of truth.
Textbook
Enderton, Herbert B, A mathematical introduction to logic, Second edition. Harcourt/Academic Press, Burlington, MA, 2001
Additional References
Goldstern, Martin and Judah, Haim, The Incompleteness Phenomenon: A New Course in Mathematical Logic, A K Peters, Ltd., Natick, MA, 1998, ISBN 1-56881-093-8.
Mendelson, Elliott, Introduction to mathematical logic, Fourth edition. Chapman & Hall, London, 1997.
Shoenfield, Joseph R, Mathematical logic, Reprint of the 1973 second printing. Association for Symbolic Logic, Urbana, IL; A K Peters, Ltd., Natick, MA, 2001
Evaluation
There will be five problem sets. Each problem set will be worth 20% of the grade.
How to contact the instructor
Office: SB 4.01.34
Telephone: 210-458-5531
Email: iovino@math.utsa.edu
Office hours: T, Th, 5-6 pm, or by appointment.
Material Covered
- 8/26: Introduction. Chapter 0
- 8/31: Section 1.1.
- 9/2: Sections 1.2 and 1.5.
- 9/7: Section 1.5
- 9/9: Section 1.5
- 9/14: Section 1.7
- 9/16: Section 1.7
- 9/21: Section 2.1
- 9/23: Section 2.2.
- 9/28: Section 2.2.
- 9/30: Secion 2.2.
- 10/5: Section 2.2.
- 10/12: Section 2.2.
- 10/21: Comments on Section 2.4.
- 10/26: Section 2.4.
- 10/28: Section 2.4.
- 11/2: Section 2.4.
- 11/4: Section 2.4.
- 11/9: Section 2.5.
- 11/11: Section 2.5.
- 11/16: Section 2.5. 11/30: Nonstandard models. 12/2: Nonstandard models.
- 8/31: Section 1.1.
