MATH 320 Set Theory (Spring 2004)

MATH 320: Set Theory

...self-evidence ... must not be confused with ... provability. --- Ernst Zermelo

• Announcements:
• Final exam is take-home and it is due on 11 June 2004, 17:30. (Questions are available as a .dvi file and a .pdf file. If you can not open these files, then you can obtain a hard-copy from my office.)
• How do mathematicians choose? - A seminar by the students of the course
• Hints to the first midterm questions:
1. a. True.
b. False.
2. a. This is in the book.
b. Take the set of integers with the usual successor function (+1) and consider f(0)=0 and f(x)=x+1.
3. a. Use the Axiom of Infinity to prove there exists at least one such set. Take the intersection of all such sets.
b. Let A be a subset of w (omega) containing the empty-set and x' whenever x is in A. By definition, w=A.
4. a. Apply induction on the set given in the hint.
b. Using (a), show that there is an order-preserving bijection between A and w.
c. Take the reverse order on w.
5. Define a map from w into the set of functions from w\{0} into w taking m to fm, where f0=id and fm+1=nfm(n).
Bonus. In naive set theory, all classes are assumed to be sets.
• The Winter issue of Matematik D�nyas� is out now and it contains a good introduction to axiomatic set theory and construction of natural numbers.
• Lectures:
Monday 15:40-17:30 (M-106) Wednesday 12:40-13:30 (M-106)
• Main Text. Notes on Set Theory by David Pierce

Reference Books: You can use any book on set theory that discusses Peano Axioms, Cardinals, Ordinals, Axiom of Choice, Well-Ordering Principle, Continuum Hypothesis.

TBA

Exams:

I am planning to make the midterm exams during the class time.

Exam 1: (Written Exam)
Date and Time: 19 April 2004 Monday, 15:40
Place: M - 106
Contents: Sections 0 - 12 (inclusive)

Exam 2: (Presentation)
Date and Time: 12 May 2004 Wednesday, 13:40
Place: Arf Hall (M - 13)
Contents: Axiom of Choice and related topics

Final: (Take-Home Exam)
Date: due on 11 June 2004 Friday, 17:30
Place: M - 242 (My office)
Contents: Everything we covered.

Make-up: (Written Exam)
Date and Time: 9 June 2004 Wednesday, 9:30
Place: M - 242
Contents: Same as the Final contents.