Ultraproducts as a tool for first-order inexpressibility in the finite and infinite

TL;DR

This paper investigates the application of ultraproducts, a classical model theory tool, to analyze inexpressibility issues in both finite and infinite first-order logic.

Contribution

It extends the use of ultraproducts to finite model theory, providing new insights into inexpressibility in finite and infinite structures.

Findings

Ultraproducts reveal limitations of first-order logic in finite structures.

New techniques for inexpressibility proofs using ultraproducts.

Bridging classical and finite model theory methods.

Abstract

Ultraproducts are a well-known tool in the classical model theory of first-order logic. We explore their uses in the context of finite model theory.