A countable structure is indivisible if for every coloring with finite range there is a monochromatic isomorphic subcopy of the structure. Each indivisible structure $\mathcal{S}$ naturally corresponds to an indivisibility problem $\mathsf{Ind}\ \mathcal{S}$, 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 $\mathsf{Ind}\ \mathbb{Q}$ and $\mathsf{Ind}\ \mathscr{E}$ from several benchmark problems, showing in particular that $\mathsf{C}_\mathbb{N} \vert_\mathrm{W} \mathsf{Ind}\ \mathbb{Q}$ and hence $\mathsf{Ind}\ \mathbb{Q}$ is strictly weaker than the problem of finding an interval in which some color is dense for a given coloring of $\mathbb{Q}$; and that the Weihrauch degree of $\mathsf{Ind}\ \mathscr{E}_k$ is strictly between those of $\mathsf{SRT}^2_k$ and $\mathsf{RT}^2_k$, where $\mathsf{Ind}\ \mathcal{S}_k$ is the restriction of $\mathsf{Ind}\ \mathcal{S}$ to $k$-colorings.

翻译：一个可数结构被称为不可分的，如果对于每个具有有限值域的染色，该结构中存在一个单色的同构子副本。每个不可分结构$\mathcal{S}$自然对应一个不可分性问题$\mathsf{Ind}\ \mathcal{S}$，该问题在给定一个表示和染色后输出这样的子副本。我们研究了两种结构的不可分性问题的魏赫劳奇复杂度：作为线性序的有理数集$\mathbb{Q}$，以及具有可数多个等价类且每个等价类包含可数多个成员的等价关系$\mathscr{E}$。我们将$\mathsf{Ind}\ \mathbb{Q}$和$\mathsf{Ind}\ \mathscr{E}$的魏赫劳奇度与若干基准问题分离开来，特别地证明了$\mathsf{C}_\mathbb{N} \vert_\mathrm{W} \mathsf{Ind}\ \mathbb{Q}$，因此$\mathsf{Ind}\ \mathbb{Q}$严格弱于在给定$\mathbb{Q}$的染色中寻找某个颜色为稠密的区间的问题；并且$\mathsf{Ind}\ \mathscr{E}_k$的魏赫劳奇度严格介于$\mathsf{SRT}^2_k$和$\mathsf{RT}^2_k$之间，其中$\mathsf{Ind}\ \mathcal{S}_k$是$\mathsf{Ind}\ \mathcal{S}$限制在$k$-染色上的情形。