论文标题
Hindman的定理在选择原则的层次结构中
Hindman's Theorem in the hierarchy of Choice Principles
论文作者
论文摘要
在$ \ Mathsf {ZF} $的上下文中，我们分析了Hindman的有限工会在无限集上的版本，通常需要证明该公理的选择。我们建立了此陈述与各种经典弱选择原则之间的含义关系，因此将陈述的强度定位为$ \ Mathsf {ac} $的弱形式。
In the context of $\mathsf{ZF}$, we analyze a version of Hindman's finite unions theorem on infinite sets, which normally requires the Axiom of Choice to be proved. We establish the implication relations between this statement and various classical weak choice principles, thus precisely locating the strength of the statement as a weak form of the $\mathsf{AC}$.
