MATH 712, Winter 2019
Topics in Foundations
The goal of this course is to introduce students to the research area of applied model theory. The particular area of application will be theories of local fields, but the techniques will be applicable to many other theories of interesting mathematical structures. I will aim to develop enough of the theory of p-adic fields to present Denef’s proof of the rationality of the Poincare series associated to the number of solutions of a p-adic polynomial equation. To take this course, a student should have seen a course in logic equivalent to Math 4L03/6L03 and a course in field theory equivalent to Math 4GR3. The required model theory and p-adic algebra will be developed through the course.
Selected topics, such as model theory, both pure and applied, general algebraic systems, set theory, proof theory, and the theory of computability.
Instructor: D. Haskell
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