Discussion questions are always due the following class day; you need not write anything down, but be prepared to talk about the question. Written homework, unless otherwise specified, is due the Monday after it is assigned. Reading. unless otherwise specified, should be done before the next class meeting.
Monday:
- Read: Chapter 1.
Optional reading (especially if the philosophical aspects of our study interest you): "The iterative conception of set," by George Boolos, in The Journal of Philosophy, available online.
- Prepare to discuss: Chapter 1, exercises 3.3 and 3.7. For 3.7, if you can, rather than just doing the exercise, state and prove a metatheorem from which the result of the exercise follows. (By a metatheorem, I mean a result that follows from the axioms, but that cannot be phrased as a theorem in the language of set theory. For example, any theorem including the phrase "For any property of sets P(x)" is a metatheorem. Such a theorem cannot be phrased as a theorem in the language of set theory, because we cannot say "for every property" in our language.) If you can do this much, your metatheorem should lead to a theorem schema (in the same sense that the Axiom of Comprehension is an axiom schema). Be as precise as possible about this theorem schema.
Also be prepared to ask any questions you have about Chapter 1.
- Write up: Class questionnaire (for Wednesday.)
|
Wednesday:
- Review: Chapter 1.
- Read: Chapter 2, sections 1, 2 and 3. We will NOT continue through the textbook at this pace; most of this material should be largely background, which we need to read to establish a common vocabulary. Also read, by next week, the in-class handout.
- Prepare to discuss: Chapter 2, exercises 1.1, 2.1 and 2.5.
- Write up: Chapter 1, exercises 3.6 (explain why this shows there is no set of all sets), 4.4 and 4.6.
|
Friday:
- Review: Chapter 2, sections 1, 2 and 3.
- Read: The rest of Chapter 2.
- Prepare to discuss: Any questions you have.
- Write up: Chapter 2, exercises 2.1 and 4.2.
|
Saturday:
- NO CLASS ON SATURDAY. We will make this up with an x-hour, perhaps next week.
|
Monday:
- Read: No additional reading.
- Prepare to discuss: Any questions you have.
- Write up: No additional homework.
|
Tuesday:
- Review: Chapter 2.
- Read: Chapter 3, sections 1 and 2.
- Prepare to discuss: Chapter 3, exercise 2.10.
- Write up: Chapter 3, exercise 2.7.
|
Wednesday:
- Review: Chapter 3, sections 1 and 2.
- Read: Chapter 3, sections 3 and 4, including the exercises.
- Prepare to discuss: Chapter 3, exercise 4.3 and 4.8.
- Write up: Chapter 3, exercises 3.2 and 4.2.
|
Friday:
- Review: Chapter 3, sections 3 and 4.
- Read: Chapter 3, section 5.
- Prepare to discuss: Any questions you have.
- Write up: Problem handed out in class, also available here.
|
Monday:
- NO CLASS ON MONDAY, MLK DAY. We will make this up with tomorrow's x-hour.
|
Tuesday:
- Review: Connections between first-order logic and set theory.
- Read: Chapter 4, sections 1 and 2.
- Prepare to discuss: Chapter 4, exercises 1.5 and 1.6.
- Write up: Chapter 4, exercise 1.7 and the problem found here.
|
Wednesday:
- Review: Chapter 4, sections 1 and 2.
- Read: Chapter 4, section 3.
- Prepare to discuss: Any questions on Chapter 4.
- Write up: Chapter 4, exercises 3.6 and 3.10.
|
Friday:
- Review: Chapter 4, section 3.
- Prepare to discuss: Any questions you have.
- Write up: Work on midterm exam due Friday, February 1.
|
Monday:
- Review: Chapter 6, section 3.
- Read: Chapter 6, sections 4 and 5.
- Prepare to discuss: Chapter 6, exercises 5.4, 5.5(a), and 5.9(a).
- Write up: Chapter 6, exercises 5.5 and 5.6.
|
Tuesday:
- Review: Chapter 6, sections 4 and 5.
- Read: Chapter 6, section 6.
- Prepare to discuss: Chapter 6, exercises 5.10, 5.11 and 5.16.
- Write up: Chapter 6, exercises 5.13 and 5.14.
|
Wednesday:
- Review: Chapter 6.
- Read: No additional reading.
- Prepare to discuss: An algorithm for multiplying ordinals in normal form. (Try to come up with one.)
- Write up: No additional written homework.
|
Friday:
- NO CLASS ON FRIDAY, WINTER CARNIVALY.
|
Monday:
- Review: Chapter 8.
- Read: Chapter 9 section 1.
- Prepare to discuss: Chapter 9, exercises 1.3 and 1.4.
- Write up: Chapter 9, exercises 1.10 and 1.13, and the following exercise: Find an infinite sequence of cardinal numbers for which the sum equals the product.
|
Wednesday:
- Review: Chapter 9, section 1.
- Read: Chapter 9, section 2.
- Prepare to discuss: Any questions you have.
- Write up: Work on midterm exam due Wednesday, February 27.
|
Friday:
- Review: Chapter 9, section 2.
- Read: Chapter 9, section 3.
- Prepare to discuss: Any questions you have.
- Write up: Work on midterm exam due Wednesday, February 27.
|
