维赫拉乌奇拉提斯的开阔的和木质的Ramsey定理 (The open and clopen Ramsey theorems in the Weihrauch lattice)

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 $\mathrm{ATR}_0$.

翻译：我们调查了Weihrauch Lattice的开放和黑白Ramsey理论的统一计算内容。虽然从反向数学的角度来看,已知这些理论相当于$\mathrm{ATR_0}美元,但并没有一种粗俗的方法把它们说成是多值功能。我们确定了8种不同的多值功能(5个相当于开放的Ramsey理论,3个相当于黑白Ramsey理论),并从Weihrauch、强力的Weihrauch和算术Weishrauch的可复制性的角度研究其程度。特别是,我们的一项功能比以前研究过的美元左右的多值函数严格强。