# Homepage of the courseForcing theory and independence proofs in mathematics

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

Prerequisites: Basic set theory (ZFC, ordinals, cardinals, transfinite induction, 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.
This book is available in the library.

## 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 or Hebrew.

1. Exercise 1: Kunen, Pages 146-147, questions 1 and 6. (Relevant definition can be found on page 95 of Kunen.)

2. Exercise 2.

3. Exercise 3:
1. Read Section 3 on pages 117--124 of Kunen's book. In particular, note Definition 3.8 and the discussion following it.
2. Homework: Kunen, page 180, Questions 5 and 6.

4. Exercise 4.

5. Exercise 5.

6. Exercise 6. Kunen, Chapter VII, Exercises (B5), (B6), (B7) [See Definition 6.12 on Page 214], (F1) [See Definition 6.7 on Page 212].

7. Exercise 7. Kunen, Chapter VII, Section 6 (pages 211 ff): Prove Lemmas 6.2, 6.3, 6.5, 6.6, 6.8, 6.9.

8. 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.
Have a fruitful study. Boaz