Set theory (Math 320) Spring 2010/11
The official text of this course is the lectures given in class. When I taught this course two years ago, I made some notes available; you can get them by following the link above. But I have some different ideas now about what to put in such notes; so I am rewriting them. I shall post here the latest version of the chapters that are ready, in the several formats:
Note that the table of contents in these notes lists more chapters than are actually provided: I am still working on those missing chapters. I may go back and edit the chapters that I have already put up here.
If you print out the notes, be careful: The page size is A5, so you can fit two of these pages on a single side of the standard A4 paper. If you do this, make sure the text is not shrunken to fit the page (this happens with some programs). Also, odd-numbered pages should be on the right (otherwise there will be a wide empty strip between two pages, but narrow outer margins).
The typeset notes here may go into things in more detail than is really needed for the course. As I said, the official text is the lectures in class!
Any textbook of axiomatic set theory will cover most of what we shall do; but different authors will have different styles and notation. I am particularly sensitive about how the natural numbers are treated.
Some of the historical background of our work is treated fictionally but compellingly in the graphic novel Logicomix.
March 18, 2011: The available text now has three chapters:
- The logic of sets
- The natural numbers
I have edited chapter 2 a lot, but mathematically it is pretty much what I posted here earlier. Chapter 3 develops ω (omega) without first defining ON (this will be defined in chapter 4). I expect to talk more about chapter 3 in class.
Here are a few exercises on what we have done so far (the comments above on printing the notes apply here):
March 25, 2011: There will be an examination in class, April 8 (at 10:40 in M-214).
April 6, 2011: The exam covers what we have done, through (and including) ordinal addition.
April 13, 2011: Exam solutions:
April 22, 2011: There will be an examination in class, May 6 (at 10:40 in M-214), on ordinal arithmetic:
- computations with normal forms;
- proofs by transfinite induction of theorems about ordinal computations.
There will be another examination on May 25, at 8:40 (the original scheduled time of the class) in M-102 (the usual place). This will cover what we do after ordinal arithmetic. The best two scores out of the three in term will count (along with the final examination) for the course grade.
Class will be cancelled, May 18 and 20.
April 28, 2011: Chapter 5 of the notes, on cardinals, was added (at the links above; Chapter 4, on ordinals, has been up for some time).
Exam solutions are here:
May 13: I have added to the exercises given above (the links are the same as here). I may add more problems soon.
May 16: I did add more problems. I do not plan on adding any more. I did however add Chapter 6, on models, to the notes at the link above. Most of that chapter is beyond the course; but we have covered in class the beginning of the chapter.
May 30: Solutions (and results) for the third exam are here:
June 15: Solutions (and results) for the final exam are here: