This mini course will give an introduction to the method of forcing. The course provides a complete proof of the independence of the Continuum Hypothesis.

Intensive course at ILLC, Amsterdam

Prof. Jouko Väänänen (University of Helsinki, University of Amsterdam)

This intensive course consists of five lectures:

Lecture DayDate TimeRoom Topics
IMon08-06-2015 14-16B0.207 A quick introduction and overview to set theory and forcing. Partially ordered sets, generic sets.
IIMon08-06-2015 16-18B0.207 Forcing names, generic extensions.
IIITue09-06-2015 14-16 D1.113 Forcing relation and its definability, Forcing Theorem.
IVTue09-06-2015 16-18 D1.113 Axioms of set theory in generic extensions. Forcing with finite conditions.
VWed10-06-2015 14-16 D1.112 Countable Chain Condition, Continuum Hypothesis.

In addition there will be homework. Homework 1. Homework 2. Homework 3. Homework is due June 20 and should be returned to the ILLC office. Students who successfully complete the course get awarded 2EC for the course.

Planned contents: With minimal set theoretic background, this mini course gives a detailed introduction to the famous mehtod of forcing, invented by Paul Cohen. The course provides a complete proof of the independence of the Continuum Hypothesis.

Prerequisites: The ILLC course Axiomatic Set Theory is an excellent background for this course.

Textbook: The lectures are self-contained, so a textbook is not needed, but the course follows Set Theory by K. Kunen, Chapter VII.

For "A taste of set theory for philosophers", see this. For a short popular article on forcing, see this.

If you want to participate, please write me an email.


Jouko Väänänen, e-mail: jouko.vaananen@helsinki.fi