独立性与逆数学中的归纳
Independence and Induction in Reverse Mathematics
AI总结：
本文研究了MAD和MED原理在逆数学中的独立性和归纳强度，揭示了这些原理与DOM原理之间的等价关系。
摘要：
我们继续受基数不变量启发的逆数学原理研究项目。本文特别关注封装存在大量相互独立对象的原理。更具体地说，我们研究了原理MAD，即存在一个最大族的 pairwise 几乎不相交集合；以及原理MED，表达存在一个最大族的函数，这些函数在某种程度上是相互不同的。我们研究这些原理及其变体的特征和关系。结果表明，归纳强度在BΣ₂⁰或IΣ₂⁰的水平上是一个关键参数；例如，在BΣ₂⁰之上，我们证明¬MAD等价于DOM原理，即每个弱表示的函数族都被某个其他函数支配。
英文摘要：
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 $\mathsf{MAD}$ stating that a maximal family of pairwise almost disjoint sets exists; and the principle $\mathsf{MED}$ 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 turns out that induction strength at the levels of $\mathsf{B}\mathrmΣ_2^0$ or $\mathsf{I}\mathrmΣ_2^0$ is an essential parameter; for instance, over $\mathsf{B}\mathrmΣ_2^0$, we show that $\neg\mathsf{MAD}$ is equivalent to the principle $\mathsf{DOM}$ expressing that every weakly represented family of functions is dominated by some other function.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
