A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often forcing constructions that add subsets to models are cited as evidence in favour of the latter. This paper informs this debate by analysing ways the Universist might interpret this discourse that seems to necessitate the addition of subsets to V. We argue that despite the prima facie incoherence of such talk for the Universist, she nonetheless has reason to try and provide interpretation of this discourse. We analyse extant interpretations of such talk, and analyse various tradeoffs in naturality that might be made. We conclude that the Universist has promising options for interpreting different forcing constructions.

中文翻译：

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强迫和集合的宇宙：我们必须失去洞察力吗？

当前关于数学基础的哲学辩论的一个核心领域是是否存在一个单一的、最大的集合论领域。宇宙主义者坚持存在这样一个宇宙，而多元宇宙主义者则认为有许多宇宙，没有一个宇宙在本体论上享有特权。通常，将子集添加到模型的强制构造被引用为支持后者的证据。本文通过分析 Universist 可能解释这种似乎需要在 V 中添加子集的话语的方式来为这场辩论提供信息。 我们认为，尽管 Universist 的此类谈话表面上不连贯，但她仍然有理由尝试并提供对 V 的解释这个话语。我们分析了对此类谈话的现有解释，并分析了可能在自然性方面做出的各种权衡。