Time & location. 1:30 - 2:50 on Tuesdays and Thursdays in SH 224
Textbook. Kenneth Kunen, Set Theory : An Introduction to Independence Proofs
Prerequisites. Students should have a background in undergraduate level set theory (e.g., 21-229) and logic, which includes a working knowledge of basic ordinal and cardinal arithmetic, Gödel's completeness theorem, and the downward Löwenheim-Skolem theorem. An understanding of the statement of Gödel's theorem on consistency proofs will also be assumed. Those without the required background should meet with the instructor as soon as possible to discuss their options.
Description. This is a relatively standard first graduate course in set theory. The two main topics are constructibility and forcing. Our primary goal is the independence of the continuum hypothesis and other statements of cardinal arithmetic. Certain aspects of infinitary combinatorics and descriptive set theory will also be central to the course. Roughly, we will cover chapters I and III-VII of the textbook in order, and refer back to chapter II as needed. The lectures and homework will include additional material not in Kunen's book. The content of the course will depend in part on whether Set Theory II (21-702) will be offered in the Spring.