Axiomatic Set Theory 2002

(New!) The answers to the take-home exam are available here.

Schedule Information

Lecturer: Dr. Marco Vervoort (email: M.R.Vervoort@uva.nl).
Level: II
UvA credits: 3.5
Trimester: 3 (April 8 - July 12)
Classes: Mondays, 11.15-13.00, Room P.015A
  Thursdays, 13.15-14.00, Room P.015A Examination: take-home exam, deadline 12 July
There will be no classes on 29/4, 2/5, 9/5, 20/5.

Course Description

Set theory according to Zermelo and Fraenkel: definitions of natural number, ordinal and cardinal and the theory of those concepts; induction, recursion; axiom of choice, continuum hypothesis, and the consistency of these principles using constructible sets.

Online Course Materials

The lecture notes and exercises are available as a PDF or postscript file (ast.pdf and ast.ps). Students are asked to read these notes as preparation for the lecture sessions, in order that the lecture sessions can focus on clarifying unclear areas, elaborating specific points, and discussion. For practice sessions, students are asked to prepare selected exercises, to discuss or present to the class.

Assignments

The lecture sessions will generally be on mondays, and the practice sessions on thursdays. Occasionally, we will deviate from this schedule. Below you find the combined list of reading and exercise assignments for the sessions:

• 8/4: Read Chapters 1 and 2
• 11/4: Exercises 2b, 3, 4, 6, 7, 11, 15.
• 15/4: Read Chapter 3, sections 1-3
• 18/4: Exercises 20, 22, 27, 28, 33 (solutions)
• 22/4: Read Chapter 3, sections 4-5
• 25/4: Exercises 36, 39, 43, 44, 45, 51 (hints and solutions)
• 29/4: No classes, but please read Chapter 4, sections 1-3
• 2/5: No classes
• 6/5: Read Chapter 4
• 9/5: No classes
• 13/5: Exercises 54, 58, 61, 64, 65, 70, 72 (hints and solutions)
• 16/5: Exercises 75, 76, 78, 85, 91, 93, 95 (hints and solutions)
• 20/5: No classes, but please read Chapter 5
• 23/5: Exercises 98, 99, 101, 103, 105, 108 (hints and solutions)
• 27/5: Read Chapter 6
• 30/5: Exercises 111, 114, 116, 120, 122 (hints and solutions)
• 3/6: Read Chapter 7, Sections 1-3
• 6/6: Exercises 124, 127, 134, 136 (hints and solutions)
• 10/6: Read Chapter 7, Sections 4-5
• 13/6: Exercises 140, 142, 150, 152, 157, 159, 160 (hints and solutions)
• 17/6: Read Chapter 7, Sections 6-8
• 20/6: Exercises 163, 166, 174, 178, 186, 197 (hints and solutions)
• 24/6: Read Chapter 8, Section 1

Examination

The examination will be a take-home exam, to be handed in on the 12th of July. The take-home exam will consist of the following assignments from the lecture notes.

1. Exercise 67 (including the generalization and an example of the Anti-Foundation Axiom).
2. Exercise 104
3. Exercise 113 (hint for part 2: countable sets of ordinals can be mapped canonically into \omega_1)
4. Exercise 146
5. Exercise 155
6. Exercise 189

(New!) The answers to the take-home exam are available here.

Feedback

I welcome comments and feedback on the sessions. You can give feedback during the sessions themselves, or send an email to M.R.Vervoort@uva.nl.