Independence in Arithmetic: The Method of $(\mathcal L, n)$-Models
Logic
2021-08-12 v3 Combinatorics
Abstract
I develop in depth the machinery of -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 . I give two applications: 1. Shelah's alternative proof of the Paris-Harrington theorem, and 2. The independence over of a new Ramsey theoretic statement about colorings of finite sequences of structures.
Cite
@article{arxiv.1906.04273,
title = {Independence in Arithmetic: The Method of $(\mathcal L, n)$-Models},
author = {Corey Bacal Switzer},
journal= {arXiv preprint arXiv:1906.04273},
year = {2021}
}
Comments
Anonymous referee found a gap in theorem 2.2. As such the main results of the paper need to be reconsidered