Model Theory of Fields

A mini-course by Piotr Kowalski (Uniwersytet Wrocławski)

First meeting and first lecture:

10:00 Thursday, February 20, 2014, Thursday, MSGSÜ Math Dept, Seminar Room (Bomonti)

Short Description:

I plan to introduce some notions of geometric model theory (Morley rank, stability) in the concrete cases of fields (with a possible extra structure). I would like to emphasize connections between algebraic geometry and model theory, both on a basic level: Ax's theorem and completeness of ACF₀, Chevalley's Theorem on Constructible Sets and elimination of quantifiers, existence of the field of definition and elimination of imaginaries; and (time permitting) on a more advanced level: Zilber's trichotomy and diophantine geometry, rationality of Poincare power series and elimination of quantifiers for p-adics.

Background needed:

Basic knowledge of commutative algebra