In set theory, a maximality principle is a principle that asserts some maximality property of the universe of sets or some part thereof. Set theorists have formulated a variety of maximality principles in order to settle statements left undecided by current standard set theory. In addition, philosophers of mathematics have explored maximality principles whilst attempting to prove categoricity theorems for set theory or providing criteria for selecting foundational theories. This article reviews recent work concerned with the formulation, investigation and justification of maximality principles.

中文翻译：

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集合论中的极大性原理

在集合论中，最大值原理是断言集合的宇宙或其某些部分的某些最大值属性的原理。集合论者已经制定了各种极大性原则，以解决当前标准集合论尚未确定的陈述。此外，数学哲学家在试图证明集合论的范畴定理或为选择基础理论提供标准的同时，也探索了极大性原理。这篇文章回顾了最近关于最大化原则的制定、调查和论证的工作。