Higher set theory
Master module V4A3
Time and location
Lecture: Monday, 14-16, Wednesday 13-15, Zeichensaal, Wegelerstra&suml;e 10.
Exercises: Monday 10-12, Seminar Room A, Beringstrasse 4, and other times
Zermelo-Fraenkel set theory (ZFC) axiomatizes the relation "x is an element of y", x ∈ y. The common mathematical notions (numbers, relations, functions, finite and infinite sequences) can be formalized by &isin-formulas, so that the basic properties of the notion can be proved from the axioms of ZFC. So the Zermelo-Fraenkel set theory provides a foundation for mathematics. In addition, the system ZFC is an axiomatization of the infinite, i.e., of general infinite numbers and structures. The most important classes of numbers in set theory are the ordinal numbers and the cardinal numbers. They satisfy remarkable arithmetic and combinatorial laws.
The lecture partially follows the first section of the standard reference Set Theory - The Third Millennium Edition by Thomas Jech, Springer Monographs in Mathematics. We shall cover chapters 1 to 6 and selected material from chapters 7 to 12.