论文标题
分区产品的编码能力
Coding power of product of partitions
论文作者
论文摘要
给定两个组合概念$ \ mathsf {p} _0 $和$ \ mathsf {p} _1 $，我们可以通过$ \ mathsf {p} _1 $编码$ \ mathsf {p} _0 $。在本次演讲中，我们解决了一个问题，$ \ mathsf {p} _0 $是整数的3色，$ \ m athsf {p} _1 $是有限的许多2颜色整数的产品。首先，我们将问题简化为引理，该问题断言某些$π^0_1 $ class of Colorings允许两个成员违反特定的组合约束。然后，我们进行了题外话，以了解班级必须多么复杂，以维持交叉约束。我们以某种方式削弱了两名成员，以解决Cholak，Dzhafarov，Hirschfeldt和Patey的一个公开问题，涉及某种Weihrauch程度的稳定的Ramsey定理。事实证明，引理的结果是$π^0_1 $ class的基础定理，并具有其他约束。我们查看了一些基础定理的几种变体，其中有些是未知的。我们最终引入了有关无限多种色彩产品的一些结果和问题。
Given two combinatorial notions $\mathsf{P}_0$ and $\mathsf{P}_1$, can we encode $\mathsf{P}_0$ via $\mathsf{P}_1$. In this talk we address the question where $\mathsf{P}_0$ is 3-coloring of integers and $\mathsf{P}_1$ is product of finitely many 2-colorings of integers. We firstly reduce the question to a lemma which asserts that certain $Π^0_1$ class of colorings admit two members violating a particular combinatorial constraint. Then we took a digression to see how complex does the class has to be so as to maintain the cross constraint. We weaken the two members in the lemma in certain way to address an open question of Cholak, Dzhafarov, Hirschfeldt and Patey, concerning a sort of Weihrauch degree of stable Ramsey's theorem for pairs. It turns out the resulted strengthen of the lemma is a basis theorem for $Π^0_1$ class with additional constraint. We look at several such variants of basis theorem, among them some are unknown. We end up by introducing some results and questions concerning product of infinitely many colorings.
