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arXiv · 2004.10482

G\"odel incompleteness through Arithmetic Universes after A. Joyal

Joost van Dijk·Alexander Gietelink Oldenziel
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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.

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Joost van Dijk, Alexander Gietelink Oldenziel. 2020-04-22. G\"odel incompleteness through Arithmetic Universes after A. Joyal. https://arxiv.org/abs/2004.10482

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