Syllabus for MATH 446

MATH 446 -- AXIOMATIC SET THEORY

SPRING 2012

Time and Room: MWF at 2:00 in MTH 0403

Instructor: Professor David W. Kueker
Office: MTH 2105
Phone: (301)405-5159
dwk@math.umd.edu
Office Hours: MW 3:00-3:50 or by appointment

Text: Yiannis Moschovakis. Notes on Set Theory, Second Edition. Springer, 2006.

Description: This course is a thorough introduction to axiomatic set theory. We will cover most of Chapters 1-5, 7-9, and 11-12 in the text. We first discuss Cantor's theory of equinumerosity from a "naïve" (= non-axiomatic) perspective. Since naïve set theory leads to paradoxes, we next introduce axioms about sets. Using the axioms we introduce various set constructions, including ordered pairs, relations, functions, the natural numbers, and arithmetic operations. We then define and study well-ordered sets, introduce the axiom of choice, and look at some of its consequences. Finally we define ordinal and cardinal numbers and arithmetic on them.

Warning: The first five chapters will be covered very rapidly. If you fall behind in the beginning it will be extremely difficult to catch up.

Course Work: There will be regular homework assignments, two one-hour exams, and a two-hour final exam. The homework assignments will be posted on this web page. The homeworks are worth a total of 100 points, the one-hour exams are worth 100 points apiece, and the final is worth 200 points, for a total of 500 points.