Weihrauch 格中的开与闭开 Ramsey 定理

有序Ramsey定理与良序保持原理在$Σ^0_2$-induction水平下的Weihrauch可约性关系：初步研究

Weihrauch reducibility between Ramsey-type theorems and well-ordering principles at the level of $Σ^0_2$-induction: A pilot study

本文研究了有序Ramsey定理与良序保持原理在$Σ^0_2$-induction水平下的Weihrauch可约性关系，并展示了其等价性及不可比性。

Ramsey's theorem and products in the Weihrauch degrees

We study the positions in the Weihrauch lattice of parallel products of various combinatorial principles related to Ramsey's theorem. Among other results, we obtain an answer to a question of Brattka, by showing that Ramsey's theorem for pairs ($\mathsf{RT}^2_2$) is strictly Weihrauch below the parallel product of the stable Ramsey's theorem for pairs and the cohesive principle ($\mathsf{SRT}^2_2 \times \mathsf{COH}$).

论加法拉姆齐定理的Weihrauch度

On the Weihrauch degree of the additive Ramsey theorem

本文用Weihrauch度刻画了与有理数和自然数着色相关的拉姆齐式定理的计算强度，证明这些原理在反推数学中多等价于$Σ^0_2$-归纳，并关联到$\mathrm{TC}_\mathbb{N}^*$与$(\mathrm{LPO}')^*$等Weihrauch度。

An inside/outside Ramsey theorem and recursion theory

Inspired by Ramsey's theorem for pairs, Rival and Sands proved what we refer to as an inside/outside Ramsey theorem: every infinite graph $G$ contains an infinite subset $H$ such that every vertex of $G$ is adjacent to precisely none, one, or infinitely many vertices of $H$. We analyze the Rival-Sands theorem from the perspective of reverse mathematics and the Weihrauch degrees. In reverse mathematics, we find that the Rival-Sands theorem is equivalent to arithmetical comprehension and hence is stronger than Ramsey's theorem for pairs. We also identify a weak form of the Rival-Sands theorem th…

Ramsey理论与算术中的边界限定

Ramsey Theory and Bounding in Arithmetic

本文探讨Ramsey定理的不同版本与模型N中算术片段F的边界方案之间的关系，通过不同框架重构并扩展Hirst的结果，讨论Weihrauch约简及等价原理。

On the Uniform Computational Content of Ramsey's Theorem

We study the uniform computational content of Ramsey's theorem in the Weihrauch lattice. Our central results provide information on how Ramsey's theorem behaves under product, parallelization and jumps. From these results we can derive a number of important properties of Ramsey's theorem. For one, the parallelization of Ramsey's theorem for cardinality $n\geq1$ and an arbitrary finite number of colors $k\geq2$ is equivalent to the $n$--th jump of weak Kőnig's lemma. In particular, Ramsey's theorem for cardinality $n\geq1$ is $Σ^0_{n+2}$--measurable in the effective Borel hierarchy, but not $Σ^…