This intensive course consists of five lectures:

Lecture | Day | Date | Time | Room | Topics |

I | Mon | 08-06-2015 | 14-16 | B0.207 | A quick introduction and overview to set theory and forcing. Partially ordered sets, generic sets. |

II | Mon | 08-06-2015 | 16-18 | B0.207 | Forcing names, generic extensions. |

III | Tue | 09-06-2015 | 14-16 | D1.113 | Forcing relation and its definability, Forcing Theorem. |

IV | Tue | 09-06-2015 | 16-18 | D1.113 | Axioms of set theory in generic extensions. Forcing with finite conditions. |

V | Wed | 10-06-2015 | 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.

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