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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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