一句话：证明若干自然拓扑空间的开集格一阶理论与二阶算术 m-等价，并刻画有效开集格理论的可判定性。
论文研究自然拓扑空间中开集构成格的一阶理论的复杂度与可判定性。作者采用可计算性与描述复杂性中的 m-等价（多一归约等价）方法，将这些理论与二阶算术、一阶算术的强度进行比较。主要结果包括：某些自然拓扑空间的开集格一阶理论与二阶算术 m-等价；对许多自然可计算度量空间和可计算 domain，其有效开集格的一阶理论不可判定；对若干重要空间，例如 ℝ^n（n≥1）与 domain Pω，该理论则与一阶算术 m-等价。这些结果从可计算性角度刻画了拓扑结构与域结构所导出开集格的一阶逻辑复杂度。
We show that the first order theory of the lattice of open sets in some natural topological spaces is $m$-equivalent to second order arithmetic. We also show that for many natural computable metric spaces and computable domains the first order theory of the lattice of effectively open sets is undecidable. Moreover, for several important spaces (e.g., $\mathbb{R}^n$, $n\geq1$, and the domain $P\omega$) this theory is $m$-equivalent to first order arithmetic.
DOI 原文 · arXiv · PDF（开放获取） · DBLP
@article{KudinovS17,
title = {First Order Theories of Some Lattices of Open Sets},
author = {Oleg Kudinov and Victor Selivanov},
journal = {Logical Methods in Computer Science},
volume = {Volume 13, Issue 3},
year = {2017},
doi = {10.23638/lmcs-13(3:16)2017}
}