NOTE

The lecture on Monday, September 20 is cancelled. I apologize for the short notice.

Moreover, the time for the exercise class has been corrected.

Forcing

This course will be lectured in English in the Autumn Term of 2004.

Course Status:

Advanced undergraduate level course worth 5 study points, recommended for students specializing in logic and wishing to deepen their knowledge of set theory.

Lectures in Autumn Term 2004:

Lectured by Doc. Taneli Huuskonen.

Lecture times: Monday, 12-2pm in C123 and Tuesday, 12-2pm in C124. Both lecture rooms are on the first floor of Exactum. The first lecture will take place on Monday, 13th September 2004. The course will be lectured in English.

Exercises:

There will be a weekly two-hour exercise class on Thursdays at 10-12 in C129. The first exercise class will take place on the September 23rd. List of exercises

Course Contents:

The subject of the course is the forcing method, which has, during its 40-year history, been the overwhelmingly most important tool for proving set-theoretical independence results. The technical basics will be covered carefully. The method will be applied to prove some classical independence results, for instance, the independence of the Continuum Hypothesis and the consistency of Martin's Axiom with the negation ofäCH.

Passing the Course:

To pass the course, the student has to take a final exam. Participation in the lectures and exercises is strictly voluntary. A final exam will be arranged on a general examination day of the Department in December 2004. There will also be later opportunities to pass the course. The exact dates will be announced later.

Material:

The course is based on the book

K. Kunen: Set Theory - An Introduction to Independence Proofs (Elsevier Science B.V. 1980)

Prerequisites:

A good general knowledge of mathematical logic and the basics of set theory is essential for following this course. The following is a rough list of topics the student should know well:

first-order formula, sentence
model, Tarski's truth definition
formal proof, Gödel's Completeness Theorem
Gödel's Incompleteness Theorems
the cumulative hierarchy of sets
the ZFC axioms
well-ordering, ordinals, ordinal induction
equipollence, cardinals
regular and singular cardinals, cofinality
the basics of cardinal arithmetics
cub and stationary sets, Fodor's lemma

Moreover, a general knowledge of the constructive hierarchy (L) and the axiom of constructivity (V=L) is useful but not necessary. Any properties of the constructive hierarchy that are used on the course will be briefly explained.

Anonymous Feedback:

You can send anonymous feedback to the lecturer during the entire course using a Web form, which you can find at the address http://www.math.helsinki.fi/kurssit/kysely/jatkuva.html. Naturally, direct feedback is also welcome, if you don't feel the need for anonymity.

Logic Courses - The Logic Group - The Department of Mathematics and Statistics