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Set Theory MAT 6973 Fall, 2006 Instructor: J. Iovino |
The course has been scheduled for Tuesdays and Thursdays, 12:30pm-1:45pm.
Prerequisites
Real Analysis I (MAT 4213) or consent of instructor.Content
The course is an introduction to the axioms of set theory, which form the foundation of all of mathematics. In many departments, this course is a standard part of the curriculum.The course is divided into four parts:
- Part 1: Fundamentals.
- The axioms of set theory, ordinals, classes and recursion, cardinals, the real numbers.
- Part 2: Well-foundedness.
- Well-founded sets and well-founded relations, the Axiom of Foundation, induction and recursion on well-founded relations.
- Part 3: Basic consistency proofs
- Absoluteness, the sets H(κ), Reflection Principles.
- Part 4: Constructibility
- Gödel's constructible universe. Gödel's proof of the consistency of the Axiom of Choice and the Generalized Continuum Hypothesis.
Textbook
Kenneth Kunen, Set Theory: An introduction to Independence Proofs, North-Holland, 1983
Additional References
Thomas Jech, Set Theory, Springer-Verlag, third edition, 2003.
Jean-Louis Krivine, Introduction to Axiomatic Set Theory, Springer, 1973.
These three textbooks are classics. Kunen's book is the most widely used set theory textbook.
Evaluation
There will be five problem sets. Each problem set will be worth 20% of the grade.
You should be ready to sustentate your solutions orally.
How to contact the instructor
Office: SB 4.02.50
Telephone: 210-458-5531
Email: iovino at math.utsa.edu
Office hours: Tuesdays and Thursdays, 5-6 pm, or by appointment.
