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arXiv · 2011.13218

Formalising Ordinal Partition Relations Using Isabelle/HOL

Mirna Džamonja·Angeliki Koutsoukou-Argyraki·Lawrence C. Paulson
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Abstract

This is an overview of a formalisation project in the proof assistant Isabelle/HOL of a number of research results in infinitary combinatorics and set theory (more specifically in ordinal partition relations) by Erd\H{o}s--Milner, Specker, Larson and Nash-Williams, leading to Larson's proof of the unpublished result by E.C. Milner asserting that for all $m \in \mathbb{N}$, $\omega^\omega\arrows(\omega^\omega, m)$. This material has been recently formalised by Paulson and is available on the Archive of Formal Proofs; here we discuss some of the most challenging aspects of the formalisation process. This project is also a demonstration of working with Zermelo-Fraenkel set theory in higher-order logic.

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BibTeXRIS

Mirna Džamonja, Angeliki Koutsoukou-Argyraki, Lawrence C. Paulson. 2020-11-26. Formalising Ordinal Partition Relations Using Isabelle/HOL. https://doi.org/10.1080/10586458.2021.1980464

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