结构上跳算子的一个不动点
A fixed point for the jump operator on structures
摘要：
假设$0^#$存在，我们证明存在一个结构，可以有效地解释自己的跳跃。特别地，我们得到一个结构$\mathcal A$，使得\[ Sp({\mathcal A}) = \{{\bf x}':{\bf x}\in Sp ({\mathcal A})\}, \]，其中$Sp ({\mathcal A})$是计算$\mathcal A$的副本的图灵度的集合。事实证明，比结果本身更有趣的是它意想不到的复杂性。我们证明了高阶算术，这是所有$n$全$n$阶算术的联合，不能证明这样的结构的存在。
英文摘要：
Assuming that $0^#$ exists, we prove that there is a structure that can effectively interpret its own jump. In particular, we get a structure $\mathcal A$ such that \[ Sp({\mathcal A}) = \{{\bf x}':{\bf x}\in Sp ({\mathcal A})\}, \] where $Sp ({\mathcal A})$ is the set of Turing degrees which compute a copy of $\mathcal A$. It turns out that, more interesting than the result itself, is its unexpected complexity. We prove that higher-order arithmetic, which is the union of full $n$th-order arithmetic for all $n$, cannot prove the existence of such a structure.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
