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

Corey Bacal Switzer

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arXiv · 1906.04273

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

Corey Bacal Switzer

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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 $\mathsf{PA}$. I give two applications: 1. Shelah's alternative proof of the Paris-Harrington theorem, and 2. The independence over $\mathsf{PA}$ of a new $\Pi^0_1$ Ramsey theoretic statement about colorings of finite sequences of structures.

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Corey Bacal Switzer. 2019-06-10. Independence in Arithmetic: The Method of $(\mathcal L, n)$-Models. https://arxiv.org/abs/1906.04273

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