# CAREER:  Model theory, independence, and approximation

> **NSF 01002526DB NSF RESEARCH & RELATED ACTIVIT** · University of Notre Dame (IN) · $524,327

## Abstract

This is a project in model theory, a branch of mathematical logic that studies the features of mathematical structures that can be expressed by formal languages. Model theory usually studies infinite structures, though, within model theory, there are techniques for taking a collection of finite structures--graphs, orders, groups, etc.--and producing an infinite limit structure that encodes useful information about the finite structures.  For example, there are Fraïssé limits, like the Rado graph or the rational order, which allow for the study of all finite graphs and orders via their rich collection of symmetries, and ultraproducts, which are logical limits that reflect the asymptotic features of a sequence of structures detected by first order logic. Some of the most striking developments in model theory concern the 'smoothly approximable' structures, a special class of structures that can be seen simultaneously as both kinds of limit, which are built out of classical geometries over finite fields and have deep connections to combinatorics and group theory. The geometries that form their basic building blocks also can be considered over infinite fields and are important objects of study in several areas of mathematics. As with the infinite limits of finite structures, model-theoretic techniques allow for the construction of infinite-dimensional limits of these (infinite but) finite-dimensional geometries and new tools are needed to understand them.  This project is focuse

## Key facts

- **NSF award ID:** 2442011
- **Awardee organization:** University of Notre Dame (IN)
- **SAM.gov UEI:** FPU6XGFXMBE9
- **PI:** Samuel Ramsey
- **Primary program:** 01002526DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** CAREER-Faculty Erly Career Dev
- **Estimated total:** $524,327
- **Funds obligated:** $99,427
- **Transaction type:** Continuing Grant
- **Period:** 07/01/2025 → 06/30/2030

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2442011

## Citation

> US National Science Foundation, Award 2442011, CAREER:  Model theory, independence, and approximation. Retrieved via AI Analytics 2026-06-06 from https://api.ai-analytics.org/grant/nsf/2442011. Licensed CC0.

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