# Applications of Model Theory

> **NSF 01002526DB NSF RESEARCH & RELATED ACTIVIT** · University of Illinois at Chicago (IL) · $119,999

## Abstract

Model theory is a part of mathematical logic which has extensive applications in other areas of mathematics and computer science. This project centers around three main projects involving model theory. The first involves solutions of differential and difference equations. These types of equations specify how an object or variable moves with respect to another in a continuous or discrete manner, respectively. Over the last decade, model theory has played a pivotal role in the resolution of several long-standing open problems for algebraic differential equations. This project aims to continue that progress as well as adapt the new methods to solutions of difference equations. The second project aims to develop connections between model theory and machine learning on both a theoretical and practical level. The third main area of this project involves applying the lessons learned from machine learning and difference equations in more general model theoretic settings. These adaptations are expected to lead to fundamental new advances in model theory. This project involves graduate student training.

Model theory has a long history of applications to transcendence results for differential equations. In the last decade, this circle of results has rapidly expanded as model theoretic methods have become more refined. This project seeks to adapt these results to the setting of difference fields, which is expected to have applications in algebraic dynamics via characterizing the invar

## Key facts

- **NSF award ID:** 2452197
- **Awardee organization:** University of Illinois at Chicago (IL)
- **SAM.gov UEI:** W8XEAJDKMXH3
- **PI:** James E Freitag
- **Primary program:** 01002526DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** —
- **Estimated total:** $119,999
- **Funds obligated:** $119,999
- **Transaction type:** Standard Grant
- **Period:** 06/15/2025 → 10/31/2026

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2452197

## Citation

> US National Science Foundation, Award 2452197, Applications of Model Theory. Retrieved via AI Analytics 2026-06-06 from https://api.ai-analytics.org/grant/nsf/2452197. Licensed CC0.

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