Offered Fall 2001
Monday and Wednesday 12:30 AM - 1:45 PM
503 Main Building (Seminar Room)
Office: 503 Main Building (corner office)
Office hours: Mondays at 11:30 AM
Exercise sessions: Wednesdays at 5:00 PM, 503 Main Building
Offices hours: by appointment
Required text: Robert L. Vaught. Set Theory: an Introduction,
Assignments (listed by due date)
|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
|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.
|Read the remainder of the first chapter of the text. You may skip
the material on the Axiom of Choice.
|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.
|Read chapter two, sections 1-3. If you are
ambitious, start on chapter 4. Try these exercises on properties of
relations from chapter one.
|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).
|Complete exercises 3, 5, 6, and 7 in chapter two,
section 3. These will be collected in class.
|You should finish reading chapter four if you have
not already done so. Start on chapter five.
|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.
exercises. They will be collected in class. Start on chapter
|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.
|Complete the Mock Final.
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.
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
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
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.