Independence and Induction in Reverse Mathematics

David Belanger, Chi Tat Chong, Rupert Hölzl, Frank Stephan
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Abstract

We continue the project of the study of reverse mathematics principles inspired by cardinal invariants. In this article in particular we focus on principles encapsulating the existence of large families of objects that are in some sense mutually independent. More precisely, we study the principle MAD stating that a maximal family of pairwise almost disjoint sets exists; and the principle MED expressing the existence of a maximal family of functions that are pairwise eventually different. We investigate characterisations of and relations between these principles and some of their variants. It will turn out that induction strength is an essential parameter in this context.
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逆向数学中的独立性和归纳法
我们将继续研究受心算不变式启发的逆向数学原理。在这篇文章中,我们特别关注那些概括了在某种意义上相互独立的对象大家族存在性的原理。更确切地说,我们研究了表示存在成对几乎不相交集合的最大族的 MAD 原则;以及表示存在成对最终不同的函数的最大族的 MED 原则。我们研究了这些原理及其一些变体的特征和它们之间的关系。事实将证明,归纳强度是这方面的一个重要参数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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