论文标题
使用isabelle/hol形式化序数分区关系
Formalising Ordinal Partition Relations Using Isabelle/HOL
论文作者
论文摘要
这是一系列研究的概述概述的许多研究导致无限制组合和集合理论（更具体地说是在序数分区关系中更具体地说是在序数分区关系中）的概述 - 米勒纳 - 米勒，Specker，Specker，Larson和Nash-Williams，导致了Larson的E.C. Milners $ MILNER SERVES $ M MILNER SERVES $ M MILNER SERTIC，以供所有$ M M M $ M M M M M M，n $ M M M M， $ω^ω\箭头（ω^ω，m）$。该材料最近已由Paulson正式化，可在正式证明的档案中获得。在这里，我们讨论了形式化过程中最具挑战性的方面。该项目也证明了与zermelo-fraenkel集理论的高阶逻辑合作。
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in ordinal partition relations) by Erdős--Milner, Specker, Larson and Nash-Williams, leading to Larson's proof of the unpublished result by E.C. Milner asserting that for all $m \in \mathbb{N}$, $ω^ω\arrows(ω^ω, m)$. 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.
