Hindman's theorem and idempotent types

TL;DR

This paper establishes an equivalence between Hindman's theorem and the existence of idempotent types within certain logical frameworks, linking combinatorial number theory with model theory.

Contribution

It proves that Hindman's theorem is equivalent to the existence of idempotent types in countable complete extensions of Peano Arithmetic, connecting combinatorics and logic.

Findings

Hindman's theorem is equivalent to the existence of idempotent types.

Idempotent types exist in countable complete extensions of Peano Arithmetic.

The result bridges combinatorial number theory and model theory.

Abstract

Motivated by a question of Di Nasso, we prove that Hindman's theorem is equivalent to the existence of idempotent types in countable complete extensions of Peano Arithmetic.