标题： 阿贝尔p-群的有效同构性 显示英文标题

标题： Effective categoricity of Abelian p-groups

摘要： 设p为一个固定的素数。 阿贝尔p-群是一个阿贝尔群（不一定是有限生成的），其中每个元素的阶都是p的某个幂。可数的阿贝尔p-群由乌尔姆定理进行分类， Khisamiev表征了具有可计算副本的阿贝尔p-群。 如果对于任何与A同构的可计算结构B，存在一个$\Delta^0_\alpha$函数来证明这两个结构是同构的，则称该可计算结构A为$\Delta^0_\alpha$范畴的。 本文旨在表征阿贝尔p-群的$\Delta^0_\alpha$范畴性，并给出了针对广泛类别的阿贝尔p-群和$\alpha$值的此类结果。 剩余的开放情况被详尽地描述了。 显示英文摘要

摘要： Let p be a fixed prime. An Abelian p-group is an Abelian group (not necessarily finitely generated) in which every element has for its order some power of p. The countable Abelian p-groups are classified by Ulm's theorem, and Khisamiev characterized the Abelian p-groups with computable copies. A computable structure A is said to be $\Delta^0_\alpha$ categorical if for any computable structure B isomorphic to A there is a $\Delta^0_\alpha$ function witnessing that the two are isomorphic. The present paper seeks to characterize $\Delta^0_\alpha$ categoricity for Abelian p-groups, and results of this kind are given for broad classes of Abelian p-groups and values of $\alpha$. The remaining open cases are exhaustively described.