G\"odel incompleteness through Arithmetic Universes after A. Joyal
Category Theory
2020-04-23 v1 Logic
Abstract
We give proofs of G\"odel's incompleteness theorems after A. Joyal. The proof uses internal category theory in an arithmetic universe, a predicative generalisation of topoi. Applications to L\"ob's Theorem are discussed.
Cite
@article{arxiv.2004.10482,
title = {G\"odel incompleteness through Arithmetic Universes after A. Joyal},
author = {Joost van Dijk and Alexander Gietelink Oldenziel},
journal= {arXiv preprint arXiv:2004.10482},
year = {2020}
}
Comments
31 pages, 4 figures