## Logic Seminar

Chieu Minh Tran

UIUC

Algebraically closed field with a multiplicatively coherent cyclic ordering

**Abstract:**We study the model theory of the structure $(\mathbb{F}; <)$ where $\mathbb{F}$ is the algebraic closure of the field of $p$ elements and $<$ is a cyclic ordering on $\mathbb{F}^\times$ induced by an injective group homomorphism $\chi: \mathbb{F}^\times \to \mathbb{C}^\times$. Various model-theoretic properties of the structure turn out to be consequences of number-theoretic behaviors of the character map $\chi$. The results obtained loosely answer a question by van den Dries, Hrushovski, and Kowalski and form parts of a program to investigate the model-theoretic properties of structures where there is a presence of randomness.

Tuesday September 5, 2017 at 4:00 PM in SEO 427