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Axiomatic Set Theory
2003/2004; 2nd Trimester
Institute for Logic, Language & Computation
Universiteit van Amsterdam

Instructor: Dr Benedikt Lwe
Grader: Brian Semmes
Time: Wednesday 3-5, Thursday 11-1
Place: P.227 (Wednesday during January), P.016 (Wednesday during February and March), P.015A (Thursday)
Course language: English
Intended Audience: Mathematics students in their third or fourth year, MoL students

Set Theory is both an area of mathematics (the study of sets as a kind of mathematical object) and an area of mathematical logic (the study of axiom systems of set theory as special axiomatic frameworks). As an area of mathematics, Set Theory has applications in all areas of pure mathematics, most notably set-theoretic topology. (Students planning to specialize in this research area, for example in the Department of Geometry at the Vrije Universiteit will greatly benefit from having a firm understanding of the basics of Set Theory.)

This course will cover the basics of axiomatic set theory presented in a mathematical fashion. Knowledge of logic is not a prerequisite, though familiarity with the axiomatic method is.

Topics covered will include:

We will start to follow the textbook Yiannis N. Moschovakis, Notes on Set Theory, Springer-Verlag 1994 which covers the first five topics. After that, we shall continue with Chapters 5, 8, 9 and 10 of Thomas Jech, Set Theory, The Third Millenium Edition, revised and expanded, Springer-Verlag 2003.

Grading will be based on weekly exercises. There will be no exam. There will be a Master level course Advanced Topics in Set Theory in the first semester of 2004/05 continuing the material of this course. It is possible to write a Master's thesis in set theory (either for an M.Sc. in Mathematics or an M.Sc. in Logic) based on the material of these two courses (Axiomatic Set Theory and Advanced Topics in Set Theory).


Additional Exercises (not part of the official homework):
Last update : March 26th, 2004