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

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 ${\Pi }_1^0$ Ramsey theoretic statement about colorings of finite sequences of structures.

arXiv commentAnonymous referee found a gap in theorem 2.2. As such the main results of the paper need to be reconsidered

References in corpus (1)

• Some Problems in Logic: Applications of Kripke's Notion of Fulfilment