Model-theoretic Elekes-Szab\'o in the strongly minimal case

TL;DR

This paper extends the Elekes-Szabó theorem to relations definable within strongly minimal structures that can be interpreted in distal structures, broadening its applicability in model theory.

Contribution

It provides a generalization of the Elekes-Szabó theorem for a wider class of structures in model theory, specifically those that are strongly minimal and interpretable in distal structures.

Findings

Generalized Elekes-Szabó theorem for strongly minimal structures

Applicable to relations definable in distal structures

Broadens understanding of definable relations in model theory

Abstract

We prove a generalizations of the Elekes-Szab\'o theorem for relations definable in strongly minimal structures that are interpretable in distal structures.