一句话：给出有效可枚举拓扑空间上 Rice-Shapiro 定理成立的条件，并构造反例刻画其失效边界。
本文研究可计算拓扑中 Rice-Shapiro 定理的适用范围。作者对有效可枚举拓扑空间提出一组条件，以保证该定理对这些空间中的可计算元素成立；进而说明若放松这些条件，就会得到 Rice-Shapiro 定理失效的有效可枚举拓扑空间类。为刻画这类空间，论文给出两种构造：一种由 wn-族生成，另一种由无可计算无穷路径的可计算树生成，并用它们构造具体例子，展示该类空间的特征。这为理解 Rice-Shapiro 定理在拓扑语义框架中的边界提供了统一视角。
We provide requirements on effectively enumerable topological spaces which guarantee that the Rice-Shapiro theorem holds for the computable elements of these spaces. We show that the relaxation of these requirements leads to the classes of effectively enumerable topological spaces where the Rice-Shapiro theorem does not hold. We propose two constructions that generate effectively enumerable topological spaces with particular properties from wn--families and computable trees without computable infinite paths. Using them we propose examples that give a flavor of this class.
DOI 原文 · arXiv · PDF（开放获取） · DBLP
@article{KorovinaK17,
title = {The Rice-Shapiro theorem in Computable Topology},
author = {Margarita Korovina and Oleg Kudinov},
journal = {Logical Methods in Computer Science},
volume = {Volume 13, Issue 4},
year = {2017},
doi = {10.23638/lmcs-13(4:30)2017}
}