Hindman's Theorem: An Ultrafilter Argument in Second Order Arithmetic

2009/06/21 by Henry Towsner, Towsner, Henry · 1 citation
Computer Science · Mathematics · #Benford’s Law and Fraud Detection #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.0906.3882

openalex publication_date 2009/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Hindman's Theorem is a prototypical example of a combinatorial theorem with a proof that uses the topology of the ultrafilters. We show how the methods of this proof, including topological arguments about ultrafilters, can be translated into second order arithmetic.

Cited by

• Π⁰₄ conservation of a Carlson-Simpson lemma for 1-variable words

Related

• Ultrafilters: Where topological dynamics = algebra = combinatorics
• Applications of Ultrafilters in Ergodic Theory and Combinatorial Number\n Theory
• A Categorical Construction of Ultrafilters
• On ultrafilter construction
• A weak variant of Hindman's Theorem stronger than Hilbert's Theorem