# Formalizing Ordinal Partition Relations Using Isabelle/HOL

@article{Damonja2021FormalizingOP, title={Formalizing Ordinal Partition Relations Using Isabelle/HOL}, author={Mirna D{\vz}amonja and Angeliki Koutsoukou-Argyraki and Lawrence Charles Paulson}, journal={Experimental Mathematics}, year={2021}, volume={31}, pages={383 - 400} }

ABSTRACT This is an overview of a formalization 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in ordinal partition relations) by Erdős–Milner, Specker, Larson and Nash-Williams, leading to Larson’s proof of the unpublished result by E.C. Milner asserting that for all , . This material has been recently formalised by Paulson and is available on the Archive of Formal Proofs; here we discuss some of the…

## 4 Citations

Formalising Szemerédi's Regularity Lemma and Roth's Theorem on Arithmetic Progressions in Isabelle/HOL

- Mathematics, Computer ScienceArXiv
- 2022

. We have formalised Szemerédi’s Regularity Lemma and Roth’s Theorem on Arithmetic Progressions, two major results in extremal graph theory and additive combinatorics, using the proof assistant…

Mathematical Proof Between Generations

- MathematicsArXiv
- 2022

. A proof is one of the most important concepts of mathematics. However, there is a striking diﬀerence between how a proof is deﬁned in theory and how it is used in practice. This puts the unique…

Wetzel: Formalisation of an Undecidable Problem Linked to the Continuum Hypothesis

- MathematicsArXiv
- 2022

. In 1964, Paul Erdős published a paper [5] settling a question about function spaces that he had seen in a problem book. Erdős proved that the answer was yes if and only if the continuum hypothesis…

Towards Formalising Schutz' Axioms for Minkowski Spacetime in Isabelle/HOL

- Computer ScienceArXiv
- 2021

A mechanisation in Isabelle/HOL of the system of axioms as well as theorems relating to temporal order is presented, particularly where the formal work required additional steps, alternative approaches, or corrections to Schutz’ prose.

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