# Axiomatic set theory 2, spring 2009

### Lecturer

### Scope: We continue with our study of forcing, through iterated forcing. We also cover Boolean-valued models of set theory. Our text is Kenneth Kunen's Set Theory.

10 cu.

### Type

Advanced studies

### Prerequisites: Introductory set theory course would be helpful, and knowledge of Kunen's text through chapter VII, section 3.

### Lectures

Weeks 3-9 and 11-18, Monday 12-14 in room BK 106 and Wednesday 14-16 in room C220.

Easter holiday 9.-15.4. ***MONDAY APRIL 27TH WE MEET AT 14:00 IN OUR USUAL ROOM***

### Exams

### Bibliography

### Registration^{}

### Exercise group

Tuesday 16-18, B322

Exercise 1: p.238,A5,A6,A7. p. 240, B5.

Exercise 2: 3 Problems: The assertion on page 208, line -8, how exactly was Zorn's lemma used? Lemma 5.13, prove in detail. Prove lemma VII, 2.17.

Exercise 3: p. 246, G1,G6. Prove lemmas 6.5,6.6,6.9 on pages 212, 213.

Exercise 4: Characterize those cardinals kappa such that kappa^

=kappa. p.240,B7,B8. p. 246, G4. (Try. There is a hint in Jech's book.)

Exercise 5: G5, p.246. H3, p. 247. (For H3, you have to read about stationary sets. See also Jech's book for this.)

EXERCISE 6, on MARCH 10: CANCELLED

Exercise 7: p. 89, 22, 23, 28, 29.

Exercise 8: 33,36,39

Exercise 9: Instructor will lecture, no homework assigned.

REMAINING EXERCISES: Instructor will lecture on Boolean-valued models, no homework assigned.