## Models of set theory I

### Master module V4A4

### Lecturers

- Prof.Dr. Peter Koepke (Lectures)
- Dr. Bernhard Irrgang (Exercises)

### Time and location

Lecture: Monday, 14-16, Wednesday 13-15, Endenicher Allee 60 006.

Exercises: Monday 10-12, EA60 107 and Friday 12-14, Beringstrasse 4 SR A.

### Contents

Transitive models of set theory, the relative consistency of the axiom of choice using the hereditarily ordinal definable sets, forcing conditions and generic filters, generic extensions, ZFC holds in generic extensions, the relative consistency of the continuum hypothesis, the relative consistency of the negation of the continuum hypothesis, iterated forcing, the relative consistency of Martin's axiom and thus of the Suslin hypothesis.

### Preliminary lecture notes

### Exercises

- Exercise Sheet, due at April 29, 2009
- Exercise Sheet, due at May 6, 2009
- Exercise Sheet, due at May 13, 2009
- Exercise Sheet, due at May 20, 2009
- Exercise Sheet, due at June 8, 2009
- Exercise Sheet, due at June 15, 2009
- Exercise Sheet, due at June 22, 2009
- Exercise Sheet, due at June 29, 2009
- Exercise Sheet, due at July 6, 2009
- Exercise Sheet, due at July 13, 2009
- Exercise Sheet, due at July 20, 2009