## Math 151 (Set Theory) Winter 2013

• Instructor: Trevor Wilson
• E-mail address: twilson@math.uci.edu
• Lectures: 15:00–15:50 MWF in 190 Rowland Hall
• Office hours 15:00–15:50 TuTh in 510V Rowland Hall (suite 510)
• Recommended textbook: Kenneth Kunen, Set Theory, ISBN 978-1-84890-050-9

### Outline of lectures, by week

1. Kunen I.3–5. Basic set-theoretic operations. Set membership and inclusion. Axioms of Extensionality, Comprehension, Pairing, and Union. The successor operation $S$, the natural numbers, and the Axiom of Infinity. Exercises.
2. Kunen I.5–7. The Axioms of Replacement and Power Set. Well-founded relations, the Axiom of Foundation, and $\in$-induction. Well-orderings and ordinals. Exercises.
3. Kunen I.7–8. More about ordinals. Order types. Exercises.
4. Kunen I.8–9. Ordinal arithmetic (addition and multiplication.) Transfinite induction and rank functions. Rank initial segments $V_\alpha$ of $V$. Exercises.
5. Kunen I.10–12. Injections, bijections, cardinals, and Hartogs numbers. The Axiom of Choice. Exercises.
6. Kunen I.12–13. Equivalent forms of the Axiom of Choice. Uninteresting cardinal arithmetic (addition and multiplication.) Review. Sample midterm.
7. Kunen I.13. Cofinality. Regular and singular cardinals. Exercises.
8. Kunen I.13, approximately. Sums and products of families of sets. Koenig's theorem (general form). Interesting cardinal arithmetic. Exercises.
9. Weakly and strongly inaccessible cardinals and $\aleph$ and $\beth$ fixed points. Measurable cardinals. Exercises.
10. Review.

### Homework policy

The homework assigned during a given week is due the next week during office hours on Tuesday. I hope that you will come to office hours in place of the discussion (which was cancelled.) If you do not come to the office hours, you may hand in the homework in class the previous day instead, or e-mail it to me as a PDF, PostScript, or DVI file.

You may get help on the homework assignment from any source you choose, including other students and the Internet. The usual standards of academic integrity apply, and in particular you must credit your collaborators and cite your sources (the exact citation format is not important.) There are only two exceptions: (1) you do not have to cite the course textbook, and (2) you do not have to credit me for any help that I give you.

A good online tool for help with math homework is the Math StackExchange website. Make sure to read the FAQ (and in particular this page) before asking a question there. If you get help from this website, make sure that your homework paper cites the web page where the question and answer appear. It is good enough to give the exact title of your question.

If you plan to turn in the homework late, you must let me know as soon as possible (which usually means before the due date) and tell me why and when you want to turn it in late. Even this does not guarantee that I will accept it.

### Grading policy

I reserve the right to tweak the following numbers by up to 10% each.
• Homework: 50%
• Participation: 5%
• Midterm exam: 20%
• Final exam: 25%
I haven't decided what will be required for the participation score, but it will be easy to get full credit on it. To calculate the course grade, the other component scores will first be adjusted to lie in the interval $[0,1]$ with an average score of about $1/2$. I will then take a sum of the adjusted scores weighted as above, yielding a single number in the interval $[0,1]$ that will be converted to a letter grade in some reasonable manner to be determined later.

The exams will be take-home and you will be permitted to refer to any written, printed, or online material that you wish, but not to consult with or seek help from any living person, either directly or indirectly. As always, you must cite your sources.