A class of Kripke frames is called modally definable if there is a set of modal formulas such that the class consists exactly of frames on which every formula from that set is valid, i. e. globally true under any valuation. Here, existential definability of Kripke frame classes is defined analogously, by demanding that each formula from a defining set is satisfiable under any valuation. This is equivalent to the definability by the existential fragment of modal language enriched with the universal modality. A model theoretic characterization of this type of definability is given.

中文翻译：

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模态框架类的存在可定义性

如果存在一组模态公式使得该类恰好由来自该集合中的每个公式都有效的帧组成，即在任何估值下全局正确，则一类 Kripke 框架被称为模态可定义的。在这里，Kripke 框架类的存在可定义性被类似地定义，通过要求定义集中的每个公式在任何估值下都是可满足的。这等价于被普遍情态丰富的情态语言的存在片段的可定义性。给出了这种可定义性的模型理论表征。