Axiomatische Verzamelingentheorie
2012/2013; 2nd Semester
Institute for Logic, Language & ComputationUniversiteit van Amsterdam
Instructor: Prof. Dr. Benedikt
Löwe
Teaching Assistants: Takanori Hida,
Zhenhao Li.
Vakcode: WI305096
ECTS: 6
Time & Place:
February & March 2013: Tuesday 15-17 (SP C1.112),
Friday 13-15 (SP C1.112)
April & May 2013: Tuesday 13-15 (SP C1.112), Wednesday
13-15 (SP F1.02)
Course language: English
Intended audience: B.Sc. students of Mathematics,
M.Sc. students of Logic.
Goal of this course: Understanding of the connections between logic and set theory, in particular the axiomatic approach. Skillful handling of ordinals and cardinals, in particular the methods of transfinite induction and recursion.
Content of the course: Axioms of Set Theory, Set Theory as a Foundations of Mathematics, Ordinal Numbers, Cardinal Numbers, Axiom of Choice. Possibly basics of some additional topics such as set theory of the reals, descriptive set theory, and large cardinals.
Prerequisites: Mathematical maturity, decent understanding of first-order logic.
Evaluation:
- Homework.
- There will be 12 to 13 homework sheets.
- You are allowed to either work alone or in a group of at most two people for the homework. It is not necessary to stay in the same group for every homework set.
- Homework is handed in either before class on the day of the deadline mentioned on the homework set or by e-mail to T.Hida(at)uva.nl. Late homework is not accepted.
- Exam. The exam will be on 22 May 2013, 13-16, USC Sporthal 2.
- Final grade. The final grade is the average of the grade of the Homework component and the Exam component calculated according to the OER regulations (Part A, Article 23).
If you do not pass the course in the first attempt, there will be a hertentamen. In those cases where it becomes necessary to redo (parts of) the homework component, we shall discuss individual solutions.
Literature.
- Keith Devlin, The Joy of Sets, amazon.co.uk
- Yiannis N. Moschovakis, Notes on Set Theory, amazon.co.uk
- Herbert B. Enderton, Elements of Set Theory, amazon.co.uk
- Heinz D. Ebbinghaus, Einführung in die Mengenlehre.
- Thomas S. Jech, Set Theory, amazon.co.uk
- Kenneth Kunen, Set Theory, amazon.co.uk
Course syllabus.
| 5 February 2013 | Hoorcollege 15-17 C1.112 | Motivation (1): Set theory as a field of mathematics, paradoxes of the infinite, definition of "of equal size", Cantor's theorem without proof, existence of transcendental numbers, transfinite procedures. Motivation (2): Set theory as a foundations of mathematics. |
|---|---|---|
| 8 February 2013 | Hoorcollege 13-15 C1.112 | Homework Set #1 |