We prove strong completeness results for some modal logics with the universal modality, with respect to their topological semantics over 0-dimensional dense-in-themselves metric spaces. We also use failure of compactness to show that, for some languages and spaces, no standard modal deductive system is strongly complete.

中文翻译：

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模态逻辑在 0 维度量空间上的强大完整性

我们证明了一些具有通用模态的模态逻辑的强完整性结果，关于它们在 0 维自身密集度量空间上的拓扑语义。我们还使用紧凑性失败来表明，对于某些语言和空间，没有标准的模态演绎系统是强完备的。