We study the computational content of various theorems with reverse mathematical strength around Arithmetical Transfinite Recursion (${\mathsf{ATR}}_0$) from the point of view of computability-theoretic reducibilities, in particular Weihrauch reducibility. Our main result states that it is equally hard to construct an embedding between two given well-orderings, as it is to construct a Turing jump hierarchy on a given well-ordering. This answers a question of Marcone. We obtain a similar result for Fraïssé's conjecture restricted to well-orderings.

中文翻译：

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井井有条之间的嵌入：可计算性理论的约简

我们围绕算术超限递归（${\mathsf{ATR}}_0$）从可计算性-理论可简化性，尤其是Weihrauch可简化性的角度来看。我们的主要结果表明，在两个给定的井次之间构造嵌入同样困难，因为要在给定的井次上构造图灵跳跃层次。这回答了马可恩的问题。对于仅限于良序的弗雷塞猜想，我们得到了相似的结果。