Model Theory of Certain Algebraic Theories

Abstract

The course provides a basic introduction to model theory which allows to understand certain model theoretic results in algebra such as Artin’s conjecture on p-adic number fields.

Prerequisite

Familiarity with basic notions in abstract algebra and basic number theory.

Syllabus

There are two parts of the course.

A. Model constructions: basic introduction to models, structures, and ultraproducts

B. Algebraic theories: model theory of groups, fields, algebraically closed valued fields, and Henselian fields.

Reference

1. Alexander Prestel and Charles Delzell “Mathematical Logic and Model Theory” in Universitext.

2. A. Prestell and P. Roquette “Lectures on Formally p-adic Fields”, Lecture Notes in Mathematics, Vol 1050, Springer (1984)

3. Marvin Greenberg “Lectures on Forms in many variables”

Lecturer Intro.

I joined BIMSA in 2023. Prior to that, I held a faculty position at University of Notre Dame from 2016 to 2023, and before that, I held postdoctoral positions at University of British Columbia and University of Texas at Austin from 2012 to 2016. I received my Ph.D in 2012 from University of Arizona. I mainly work in arithmetic geometry and algebra.