A countable structure is indivisible if for every coloring with finite range there is a monochromatic isomorphic subcopy of the structure. Each indivisible structure naturally corresponds to an indivisibility problem which outputs such a subcopy given a presentation and coloring. We investigate the Weihrauch complexity of the indivisibility problems for two structures: the rational numbers $\mathbb{Q}$ as a linear order, and the equivalence relation $\mathscr{E}$ with countably many equivalence classes each having countably many members. We separate the Weihrauch degrees of both corresponding indivisibility problems from several benchmarks, showing in particular that the indivisibility problem for $\mathbb{Q}$ cannot solve the problem of finding a monochromatic rational interval given a coloring for which there is one; and that the Weihrauch degree of the indivisibility problem for $\mathscr{E}$ is strictly between those of $\mathsf{RT}^2$ and $\mathsf{SRT}^2$, two widely studied variants of Ramsey's theorem for pairs whose reverse-mathematical separation was open until recently.

翻译：一个可数结构称为不可分的，若对每个有限值域染色，该结构都存在同构的单色子复制。每个不可分结构自然对应一个不可分性问题，该问题给定该结构的一个呈现与染色，输出这样一个子复制。我们研究两个结构的不可分性问题的魏劳赫复杂度：作为线性序的有理数集$\mathbb{Q}$，以及具有可数个等价类且每个等价类有可数多个成员的等价关系$\mathscr{E}$。我们将这两个相应不可分性问题的魏劳赫度与若干基准分离开来，特别地表明：$\mathbb{Q}$的不可分性问题无法求解在存在单色有理区间的染色中寻找这样一个区间的问题；$\mathscr{E}$的不可分性问题的魏劳赫度严格介于$\mathsf{RT}^2$与$\mathsf{SRT}^2$之间——这是拉姆齐定理对于数对的两种广泛研究的变体，其反向数学分离问题直到近期才获解决。