Modal logic has been used to analyze potential infinity and potentialism more generally. However, the standard analysis breaks down in cases of divergent possibilities, where there are two or more possibilities that can be individually realized but which are jointly incompatible. This paper has three aims. First, using the intuitionistic theory of choice sequences, we motivate the need for a modal analysis of divergent potentialism and explain the challenges this involves. Then, using Beth–Kripke semantics for intuitionistic logic, we overcome those challenges. Finally, we apply our modal analysis of divergent potentialism to make choice sequences comprehensible in classical terms.

中文翻译：

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发散潜能论：一种应用于选择序列的模态分析

模态逻辑已被用于更普遍地分析势无穷和势论。然而，标准分析在不同可能性的情况下失效，其中有两个或多个可以单独实现但共同不相容的可能性。本文有三个目的。首先，使用选择序列的直觉主义理论，我们激发了对发散潜力主义进行模态分析的需求，并解释了其中涉及的挑战。然后，将 Beth-Kripke 语义用于直觉逻辑，我们克服了这些挑战。最后，我们应用我们对发散势论的模态分析，使选择序列可以用经典术语来理解。