Topics: This is an introductory course in mathematical logic at the graduate level. Topics to be covered during the Fall quarter to include first order logic, soundness, completeness, cut-elimination, Herbrand's theorem, decidability, undecidability, Robinson resolution, Lowerheim-Skolem, Craig interpolation, quantifier elimination, elementary embeddings, model completeness, preservation theorems.

There are no particular prerequisites beyond sufficient mathematical maturity. Suitable for graduate students in mathematics, computer science, philosophy. Please email me if you are interested in attending and cannot make the first lecture. (Thurs, Sep 26).

There is no textbook. Supplemental reading includes:

For Proof Theory:
Handbook of Proof Theory, chapters 1 and 2 by the instructor.(Available freely online.)
Proof Theory, by Gaisi Takeuti. (Low-priced Dover edition available.)
For Model Theory:
A Shorter Model Theory by Wilfrid Hodges. (Dover edition available)
Model Theory (Chang and Keisler) is a bit more advanced.

In this talk we apply Fourier analysis of Boolean functions to solve problems in social choice theory and property testing. In particular we examine Arrow's impossibility theorem and the BLR test.