MATH 6730, ADVANCED SET THEORY
Prof. Monk
Spring 2008
Web page updated April 28, 2008: Solutions, Chapter13.
Web page updated April 19, 2008: Solutions, Chapter12.
OH: M2, W10, F10 or by appointment.
email: don.monk@colorado.edu
Files for downloading are underlined below, and are in .pdf form.
There is no textbook for this course, and no examinations. Lecture notes will
be posted on this web page periodically. The course grade
will be based on assigned exercises. After the exercises are returned you can
try again on those with mistakes, for two weeks after the original due date.
A total score of 75\% is needed for an A, 50\% for a B.
Solutions to all exercises found in the notes will be posted on this web page
periodically, and exercises cannot be turned in after the solutions are
posted.
If you want to look at a more elementary treatment, the following book
is on one-day reserve in the math-physics library:
Enderton, Elements of Set Theory.
For a large part of the notes, I will follow portions of
Kunen, Set theory,
which is also on reserve. A more comprehensive treatment of advanced
set theory is found in
Jech, Set theory, third edition,
which is also put on reserve.
LECTURE NOTES:
Table of contents
Chapter 1: The logic underlying set theory
Chapter 2: The axioms, and elementary set theory
Chapter 3: ordinals
Chapter 4: well-founded induction and recursion
Chapter 5: ordinal arithmetic
Chapter 6: cardinal arithmetic
Chapter 7: universes and relativization
Chapter 8: absoluteness, and the relative consistency of the non-existence of
inaccessibles
Chapter 9: generic extensions
Chapter 10: forcing, and ZFC in M[G]
Chapter 11: relative consistency of not(CH)
Chapter 12: constructibility, and the relative consistency of AC plus GCH
Chapter 13: clubs and stationary sets
Chapter 14: Martin's axiom
Chapter 15: embeddings, iterated forcing, and the relative consistency of MA
plus not(CH)
Chapter 16: Powers of regular cardinals
Errata no. 1.
Errata no. 2.
Errata no. 3.
Errata no. 4.
Errata no. 5.
Errata no. 6.
Errata no. 7.
Errata no. 8.
Errata no. 9.
Errata no. 10
EXERCISES:
Due Friday, January 25: Chapter 1, E1.1, E1.2, E1.3, E1.4.
Due Friday, February 1: Chapter 2: E2.5; Chapter 3: E3.1, E3.2, E3.3.
Due Friday, February 8: Chapter 4: E4.1, E4.2; Chapter 5: E5.2, E5.3.
Also, final due date for Chapter 1 exercises.
Due Friday, February 15: Chapter 6: E6.1, E6.3, E6.5, E6.7. Also, final due
date for Chapter 2,3 exercises.
Due Friday, February 22: Chapter 7: E7.1, E7.2, E7.4, E7.5. Also, final due
date for Chapter 4,5 exercises.
Due Friday, February 29: Chapter 8: E8.1, E8.2, E8.3, E8.4. Also, final due
date for Chapter 6 exercises.
Due Friday, March 7: Chapter 9: E9.1, E9.2, E9.3, E9.4. Also, final due date
for Chapter 7 exercises.
Due Friday, March 14: Chapter 10: E10.2, E10.3, E10.4, E10.7.
Also, final due date
for Chapter 8 exercises.
Due Friday, March 21: Chapter 11: E11.3, E11.4, E11.5, E11.6.
Also, final due date
for Chapter 9 exercises.
Due Friday, April 4: Chapter 12: E12.1, E12.2, E12.3, E12.4. Also, final due
date for Chapter 10 exercises.
Due Friday, April 11: Chapter 13: E13.1, E13.2, E13.3, E13.4. Also, final due
date for Chapter 11 exercises.
Due Friday, April 18: Chapter 14: E14.2, E14.4, E14.5, E14.6 (last assignment;
final due date later). Also, final due date for Chapter 12 exercises.
Due Friday, April 25: final due date for Chapter 13 exercises.
Final due date for Chapter 14 exercises: In my office, mail box, or email by
Wednesday, May 7 at 4pm.
Index of words (updated when new chapters are posted)
Index of symbols (updated when new chapters are posted)
Solutions to exercises in Chapter 1.
Solutions to exercises in Chapter 2.
Solutions to exercises in Chapter 3.
Solutions to exercises in Chapter 4.
Solutions to exercises in Chapter 5.
Solutions to exercises in Chapter 6.
Solutions to exercises in Chapter 7.
Solutions to exercises in Chapter 8.
Solutions to exercises in Chapter 9.
Solutions to exercises in Chapter 10.
Solutions to exercises in Chapter 11.
Solutions to exercises in Chapter 12.
Solutions to exercises in Chapter 13.