Homepage of the course An introduction to Forcing theory

Mondays 14:00-16:00, Ziskind 261.

Important notice! If you are not in the course's mailing list, please let me know immediately (email me your email address which you use most frequently). Important announcements (like errors in exercises, cancellation of a lecture, etc.) will be emailed only to the mailing list.

Prerequisites: Basic set theory (ZFC, ordinals, cardinals, transfinite induction, etc.); Undergraduate mathematical logic (models, proofs, completeness theorem, etc.).

Recommended reading: Kenneth Kunen, Set Theory: An introduction to independence proofs. Small parts of this book will be available in electronic format, for personal usage by the students only. Contact me for more details.

Exercises

Frequency. Exercises are given each week, and are to be handed in the lecture of the following week. I will try to make the exercises availabe on this webpage on the same day of the lecture (email me if you cannot find them).

Language. Exercises must be written in English.

  1. 12 Mar 07.

  2. 19 Mar 07. Reading: Kunen, pages 117--124.
    Note differences in notation: \phi^M for "M \models \phi", R(\alpha) for V_\alpha.

  3. 26 Mar 07. Reading: Kunen, pages 165–169.

  4. 16 Apr 07.

  5. 30 Apr 07.

  6. 30 Apr 07.

  7. 14 May 07: Kunen, Chapter VII, Exercises (B5), (B6), (B7) [See Definition 6.12 on Page 214], (F1) [See Definition 6.7 on Page 212].

  8. 25 Jun 07: Kunen, Chapter VII, prove Lemmas 6.2, 6.3, 6.5, 6.6, 6.8, 6.9.

  9. Final work: Kunen, Chapter VII, Exercises G1, G4, G6, H21, H22.
    In G4, it suffices to prove the case I=omega_1 x omega. Hint: The generic function gives a list of aleph_1 many reals, and by density, each real in the extension appears in this list.

Lecture notes

I decided to make my personal lecture notes available, despite there being some mistakes here which I do not plan to fix in the near future. All these are easy to detect, and the notes should be useful nonetheless.

Lecture notes on Ramsey Theory

This is not related to the course, nor needed for the course, but every mathematician should have a look at this fascinating material!

First lecture.
Second lecture.
Third lecture.
Fourth lecture.
Fifth lecture.