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Advanced Topics in Set Theory
2003/2004; 1st Semester
Institute for Logic, Language & Computation
Universiteit van Amsterdam

Instructor: Dr Benedikt Lwe
Vakcode: MolATST6
Time: Tuesday 3-5
Place: P.015B
Course language: English
Intended Audience: MoL students, Mathematics students in their fourth year
Prerequisites: This course assumes knowledge comparable to the course "Axiomatic Set Theory".

Building on the basics of set theory, we can further investigate properties of the set-theoretic universe. Some of the techniques used are very important in several areas of mathematics. We will also look at infinite games, their set-theoretic properties and the way they connect topology, descriptive set theory, logical foundations of mathematics and game theory proper.

The course will cover selected chapters from Akihiro Kanamori's book The Higher Infinite. In particular, the course will cover the following topics:

Reprise of large cardinal material from "Axiomatic Set Theory": inaccessible cardinals, Mahlo cardinals, weakly compact cardinals, Ramsey cardinals, measurable cardinals; normal ultrafilters; Basic Theory of the constructible universe L; Partition Cardinals and Structures; 0#; Descriptive Set Theory; Basics of Set-Theoretic Game Theory; Homogeneously Suslin Sets; Higher Determinacy


Topics covered so far:


Homework:

  1. Homework Set #1 (Warm-up exercises). Deadline: September 16th, 2003.
  2. Homework Set #2 (Measurable cardinals and constructibility). Deadline: September 30th, 2003.
  3. Homework Set #3 (Constructibility and partition relations). Deadline: October 28th, 2003.
  4. Homework Set #4 (Partition relations and cardinals). Deadline: November 11th, 2003.
  5. Homework Set #5 (Borel sets). Deadline: November 18th, 2003.
  6. Homework Set #6 (Set theory of the reals). Deadline: November 25th, 2003.
  7. Homework Set #7 (Suslin property). Deadline: December 2nd, 2003.
  8. Homework Set #8 (Determinacy). No Deadline: This homework set doesn't count for the grade.

Last update : Dcember 11th, 2003