24.243 Classical Set Theory
Spring 2007
Instructor: Vann McGee
Lecture: WF1.30-3 (32-D831)
Information:
Set theory was invented by Georg Cantor, who extended
traditional number theory by allowing infinite numbers. Here we’ll
begin by developing the basic laws of infinite numbers the way
Cantor did, reasoning informally by the ordinary methods of
mathematics. In the long run, however, we’ll want to set our work
on a more rigorous foundation, because in set theory informal
mathematical methods are liable to stumble into paradoxes. So we’ll
go back and develop the theory rigorously, on the basis of the
axioms of Zermelo-Fraenkel set theory. I hope to get as far a
proving the consistency and independence of the continuum
hypothesis. No previous acquaintance with set theory will be
assumed.
I wanted to use Kenneth’s Kunen’s Set Theory as
a textbook, but I found out at the last minute that it’s out of
print. (Amazon.com had it in stock when I sent in my textbook
order.) So we’ll use a combination of sections from Kunen’s book,
sections from Frank Drake’s book (also titled Set Theory), and
typewritten notes. To start out, I’m putting Chapter One of Kunen’s
book on the Stellar site.. More or less, we’ll cover the material
in the first six chapters of Kunen, skipping Chapter Two.
There will be homework assignments, usually one
a week, posted here. There will be no final exam.
My regular office hours are Tuesdays from 5 to 7
in room 32-D931, but I’m around other times if that’s not
convenient for you. My e-mail address is vmcgee@mit.edu, and my
phone number is 617-253-6394.
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