目前还没有对decipherable可呈现结构进行分类
There is no classification of the decidably presentable structures
摘要：
一个可计算结构$\mathcal{A}$是可判定的，如果给定一个初等一阶逻辑公式$φ(\bar{x})$和一个元组$\bar{a} \in \mathcal{A}$，我们有一个判定过程来判定$φ$是否为$\bar{a}$ .我们发现，有没有合理的分类decipherable可呈现结构。形式上，我们证明了具有可判定表示的可计算结构的索引集是$Σ^1_1$ -完备的。即使我们把注意力限制在组、图或场上，这个结果也是成立的。我们还证明了对于任何$n$，具有$n$ -可判定表示的可计算结构的索引集都是$Σ^1_1$ -完全的.
英文摘要：
A computable structure $\mathcal{A}$ is decidable if, given a formula $φ(\bar{x})$ of elementary first-order logic, and a tuple $\bar{a} \in \mathcal{A}$, we have a decision procedure to decide whether $φ$ holds of $\bar{a}$. We show that there is no reasonable classification of the decidably presentable structures. Formally, we show that the index set of the computable structures with decidable presentations is $Σ^1_1$-complete. This result holds even if we restrict out attention to groups, graphs, or fields. We also show that the index sets of the computable structures with $n$-decidable presentations is $Σ^1_1$-complete for any $n$.
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。
