SET THEORY
Offered Fall 2001
Monday and Wednesday 12:30 AM - 1:45 PM
503 Main Building (Seminar Room)

Assignments (listed by due date)

Monday, September 10th:	Read sections 1-5 of the text. Try a few of the exercises. Particular attention should be paid to exercises 1.3, 1.4, 4.3, 5.5-9 in chapter one. These will be discussed in the Wednesday evening session.
Wednesday, September 19th:	Read the remainder of the first chapter of the text. You may skip the material on the Axiom of Choice. (We will return to it later.) The problem session for this week will be Thursday at 6:00 PM, instead of the usual day and time.
Monday, September 24th:	Read the remainder of the first chapter of the text. You may skip the material on the Axiom of Choice.
Wednesday, September 26th:	Start reading chapter two of the text. Complete exercises 1.7.3, 1.8.1, and 1.8.3. These will be collected in class. The problem session this week will be (was) Tuesday September 25th at 6:00 PM instead of the usual day and time.
Monday, October 1st:	Read chapter two, sections 1-3. If you are ambitious, start on chapter 4. Try these exercises on properties of relations from chapter one.
Wednesday, October 3rd:	Continue reading chapter 4. For exercises, prove some of the simple arithmetic properties of cardinal numbers (listed in the various propositions of sections 1-3 of chapter two).
Wednesday, October 10th:	Complete exercises 3, 5, 6, and 7 in chapter two, section 3. These will be collected in class.
Monday, October 22nd:	You should finish reading chapter four if you have not already done so. Start on chapter five.
Wednesday, October 24th:	This is the promised alternate problem set. You may complete it for a grade (due the 24th). Only the higher of the grades for this and the previous problem set will count toward your final grade.
Wednesday, October 31th:	Complete these exercises. They will be collected in class. Start on chapter 6.
Wednesday, November 14th:	Complete exercises 1.1 and 2.2, 2.5, and 2.7 (second part) in chapter 5. They will be collected in class. Begin reading chapter 7.
Wednesday, November 28th:	Complete these exercises on well-orders. Note: this is a revised version. They will be collected in class. Continue reading chapter 7, and focus on sections 3 and 5.
Monday, December 3rd:	Complete the Mock Final.

Supplementary Material

• Course Description.
• A Short Guide to Further Reading on Set Theory.
• Handout for Lecture 1: A Short History of Set Theory.
• Handout for Lecture 2: The Basics of Sets, Relations, and Functions.
• Handout for Lecture 3: Structure and Order.
• Exercises on the Properties of Relations.
• Exercises on Cardinal Arithmetic.
• Exercises on Cardinals.
• Exercises on Well-Orders.

Course Description

This course is an introduction to the fundamentals of set theory. The emphasis will be on the technical material, although there will be some philosophical discussion.

Topics to be covered will include: the standard axioms of set theory; the basic operations on sets (union, intersection, power set etc); the theory of ordinal and cardinal numbers (basic properties, transfinite induction, ordinal and cardinal arithmetic); the axiom of choice and its equivalents; the cumulative hierarchy; and (if there is time) large cardinals and the proofs of independence.

Prerequisites

The course will start from scratch; no background in mathematics or logic is strictly required. However, a background in logic will be helpful; and a certain degree of technical sophistication will be essential.

Course Format

We will more-or-less go through the chapters of the text in order. It is very important for students to do the reading in advance and to do the weekly assignments. Half of these will be handed in for grading. The weekly exercise section is optional, but strongly recommended.

Evaluation

Evaluation will be based upon the mid-term (20%), the final (30%) and the assignments to be set throughout the term (50%). No late assignments will be accepted. For each student, the lowest grade on the assignments will be dropped.