论文标题
Weihrauch晶格中的开放式粘土Ramsey定理
The open and clopen Ramsey theorems in the Weihrauch lattice
论文作者
论文摘要
我们研究了Weihrauch晶格中开放式Ramsey定理的均匀计算内容。虽然从反向数学的角度来看，虽然它们相当于$ \ mathrm {atr_0} $，但没有一种规范的方式可以将它们作为多相关函数表达。我们确定了8个不同的多相关函数（对应于开放的Ramsey定理和3个对应于Clopen Ramsey定理的功能），并从Weihrauch的角度，强烈的Weihrauch和Arithmetic Weihrauch降低性来研究它们的程度。特别是，我们的功能之一比$ \ mathrm {atr} _0 $引起的任何先前研究的多价函数都严格强。
We investigate the uniform computational content of the open and clopen Ramsey theorems in the Weihrauch lattice. While they are known to be equivalent to $\mathrm{ATR_0}$ from the point of view of reverse mathematics, there is not a canonical way to phrase them as multivalued functions. We identify 8 different multivalued functions (5 corresponding to the open Ramsey theorem and 3 corresponding to the clopen Ramsey theorem) and study their degree from the point of view of Weihrauch, strong Weihrauch and arithmetic Weihrauch reducibility. In particular one of our functions turns out to be strictly stronger than any previously studied multivalued functions arising from statements around $\mathrm{ATR}_0$.
