Math 561 - Set Theory

Lectures: TuTh 9:45-11:00am, Room 106 McAllister
Instructor: Jan Reimann
Office: 318B McAllister
Office hours: Tu 11-12, We 10-11
Email:
Personal Website: http://math.psu.edu/reimann/

The goal of this course is to prove the independence of the continuum hypothesis. We will develop all necessary tools along the way: Basic notions and techniques of model theory, Axioms of ZF, the constructible universe L, and Cohen's forcing method. If time permits, we will also discuss Solovay's model in which every set of reals is measurable.

Most of the material is covered in T. Jech, Set Theory. An online version of the book is available for Penn State members (use a campus computer or the VPN server) at dx.doi.org/10.1007/3-540-44761-X

Recommended reading: Some topics are treated rather succinctly in Jech. We will supplement these by the following books.

• D. Marker, Model Theory - An Introduction, Springer, 2002
  (also available online dx.doi.org/10.1007/b98860)
• K. Kunen, Set theory: an introduction to independence proofs, North Holland, 1980

There will be a take home final at the end of the semester.

Homework will be assigned each week and will be due the following week in class. Homework will be graded and the two lowest scores will be dropped. Late homework will not be accepted. There will be no exception to this rule. Of course it may happen that you cannot turn in homework because you were ill or for some other valid reason. This is why the two lowest scores will be dropped.

The final grade will be determined as follows: 70% homework, 30% final exam.

All Penn State Policies regarding ethics and honorable behavior apply to this course.

Collaboration: Collaboration among students to solve homework assignments is welcome. This is a good way to learn mathematics. So is the consultation of other sources such as other textbooks. However, every student has to hand in an own set of solutions, and if you use other people's work or ideas you have to indicate the source in your solutions.
(In any case, complete and correct homework receives full credit.)