This article explores the connection between Boolean-valued class models of set theory and the theory of arbitrary objects in roughly Kit Fine’s sense of the word. In particular, it explores the hypothesis that the set-theoretic universe as a whole can be seen as an arbitrary entity. According to this view, the set-theoretic universe can be in many different states. These states are structurally like Boolean-valued models, and they contain sets conceived of as variable or arbitrary objects.

中文翻译：

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作为任意对象的布尔值集

本文探讨了集合论的布尔值类模型与大致 Kit Fine 意义上的任意对象理论之间的联系。特别是，它探讨了这样的假设：集合论宇宙作为一个整体可以被视为一个任意实体。根据这种观点，集合论宇宙可以处于许多不同的状态。这些状态在结构上类似于布尔值模型，并且它们包含被视为变量或任意对象的集合。