Epstein语义：刻画、插值、不可定义性与（不）完全性
Epstein Semantics: Characterization, Interpolation, Undefinability, and (In)Completeness
AI总结：
本文利用S-集构造等模型论方法研究Epstein语义，证明了模型等价类的不可数性、逻辑的S-集不变刻画、若干关系的不可定义性及相应逻辑的有限公理化，并建立了不可数多个不完全逻辑的存在性与广义Epstein模型逻辑的插值性质。
摘要：
本文是对Epstein语义的数学研究。本文的主要工具之一是（Krawczyk 2022）中引入的模型论S-集构造。我们利用它证明了若干结果：1）每个Epstein模型都有不可数多个等价的Epstein模型；2）广义Epstein模型的逻辑是CPL的S-集不变片段（类似于著名的模态逻辑van Benthem刻画定理）；3）若干Epstein关系集合是不可定义的；4）不可定义关系集合的逻辑可以被有限公理化。我们还使用其他技术证明了：5）存在不可数多个Epstein不完全逻辑；6）广义Epstein模型的逻辑具有插值性质。
英文摘要：
This paper is a mathematical investigation on Epstein semantics. One of the main tools of the present paper is the model-theoretic S-set construction introduced in (Krawczyk 2022). We use it to prove several results: 1) that each Epstein model has uncountably many equivalent Epstein models, 2) that the logic of generalised Epstein models is the S-set invariant fragment of CPL (analogon of the celebrated van Benthem characterization theorem for modal logic), 3) that several sets of Epstein relations are undefinable, 4) that logics of undefinable sets of relations can be finitely axiomatised. We also use other techniques to prove: 5) that there is uncountably many Epstein-incomplete logics and that 6) the logic of generalised Epstein models has the interpolation property.
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