Office hours: Wednesday 11 AM - 12 PM or by appointment. Let me know after class if you plan to come.
Course description:
This is the standard graduate course on axiomatic set theory beginning at the level of ordinal and cardinal arithmetic and ending with a thorough introduction to forcing and independence proofs.
Topics
The axioms of set theory
Ordinal and cardinal arithmetic
The axiom of foundation
Relativisation, absoluteness and reflection
Ordinal definable sets and inner models of set theory
The constructible universe
Cohen's method of forcing
Independence of the axiom of choice and the continuum hypothesis
Selected topics in forcing
Literature:
The standard textbook on the topic is Kenneth Kunen's: Set Theory, An Introduction To Independence Proofs (Studies in Logic and the Foundations of Mathematics), which covers almost all of the material that we go through in class. However, a more elegant presentation can be found in Jean-Louis Krivine's: Theorie des Ensembles, which unfortunately is only available in french. The presentation in class will be compatible with both of these. I also plan to make my lecture notes available on this page as they get written over the semester.
