Math 513A:  Modern Set Theory
M. Scott Osborne

Spring 2000, MWF 12:30-1:20

In the last 20 years or so, there has been a minor revolution in the teaching of set theory.  Devlin [1979] and Vaught [1985] started it, and it continued with Devlin [1993] and Just and Weese [1996].  The idea is that the style should be that of naive set theory (exemplified by the classic text of Halmos [1960]), but the content should be what is normally treated in axiomatic set theory.  For example, classes can be discussed, and ordinal numbers appear earlier.

There is much to be gained from this approach.  Zorn's lemma actually has an intuitive proof, for instance.  Also, in the olden days, folks like your prof had few ways of learning what classes really were without first acquiring plenty of mathematical logic, and classes are unavoidable in, e.g., category theory.

This course will be based on the first three chapters of Devlin [1993], which will serve as a text.  (Just and Weese [1996] is recommended as supplementary reading, but it uses too much mathematical logic for this course.  Further material will be included if time permits.  A bit of logic is required, but only a bit, and that will be covered as needed.

Prerequisites are minimal, but at least two quarters of a graduate mathematics course sequence are recommended, simply to provide some experience at graduate level mathematics.  (This is the same reason that calculus is a prerequisite for linear algebra.)

[1960] Halmos, Paul. Naive Set Theory.
[1979] Devlin, Keith. Fundamentals of Contemporary Set Theory.
[1985] Vaught, Robert.  Set Theory.
[1993] Devlin, Keith.  The Joy of Sets.
[1996] Just, Winfried, and Weese, Martin.  Discovering Modern Set Theory, I.