Set Theory

Credits 8 credit points
Instructors Hart, K.P. (Technische Universiteit Delft), Löwe, B. (Universiteit van Amsterdam)
The course is a combination of an introductory and an advanced course in set theory. The first seven weeks are an introduction to axiomatic set theory, and so the course can be followed by a student who has no axiomatic set theory background. We will however assume mathematical maturity, including the naive use of sets that is very common in mathematics.
To provide the students with a basic knowledge of axiomatic and combinatorial Set Theory, both in preparation of further study of the subject and to provide tools that are useful in disciplines such as General Topology, Algebra and Functional Analysis.
The course will start with an introduction to axiomatic Set Theory, based on the axioms of Zermelo and Fraenkel. It will show how the generally well-know facts from naïve Set Theory follows from the axioms and how modern mathematics can be embedded in Set Theory.

The second part of the course will offer combinatorial tools from Set Theory that have proved useful in infinitary situations in Algebra, Topology and Analysis. 
We offer a choice from
    - Partition Calculus: the theorems of Ramsey, Erdös-Rado and others
    - Combinatorial properties of families of subsets of the natural numbers
    - Trees, stationary sets, the cub filter
    - PCF theory
    - Large cardinals 
Organization Three-hours lectures.
Written exam on June 22, 2011; 13:00-16:00h in Unnik, room Groen, and homework assignments; both will account for 50% of the final grade.
We recommend the following books
  - T. Jech, Set Theory. The Third Millenium Edition,     
  - K. Kunen, Set Theory. An introduction to Independence proofs.
  - Y. N. Moschovakis, Notes on Set Theory,      
  - K. J. Devlin, The Joy of Sets.
Remarks Please visit the website.
  Last changed: 02-03-2015 09:09