We characterise the existentially closed models of the theory of exponential fields. They do not form an elementary class, but can be studied using positive logic. We find the amalgamation bases and characterise the types over them. We define a notion of independence and show that independent systems of higher dimension can also be amalgamated. We extend some notions from classification theory to positive logic and position the category of existentially closed exponential fields in the stability hierarchy as NSOP 1 but TP 2 .

中文翻译：

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存在闭指数场

我们描述了指数场理论的存在性封闭模型。它们不构成初级班级，但可以使用正逻辑进行研究。我们找到合并基础并描述它们的类型。我们定义了一个独立的概念，并表明更高维度的独立系统也可以合并。我们将一些概念从分类理论扩展到正逻辑，并将稳定性层次结构中存在闭指数场的类别定位为 NSOP 1 但 TP 2 。