Independence in Arithmetic: The Method of (\mathcal L, n)-Models

2019/06/10 by Corey Bacal Switzer, Switzer, Corey Bacal
Computer Science · Mathematics · #03C62 #03C98 #05D10 #Advanced Topology and Set Theory #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge

paper · pdf · doi:10.48550/arxiv.1906.04273

openalex publication_date 2019/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

I develop in depth the machinery of (\mathcal L, n)-models originally introduced by Shelah and, independently in a slightly different form by Kripke. This machinery allows fairly routine constructions of true but unprovable sentences in PA. I give two applications: 1. Shelah's alternative proof of the Paris-Harrington theorem, and 2. The independence over PA of a new Π⁰₁ Ramsey theoretic statement about colorings of finite sequences of structures.

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