It is a striking fact from reverse mathematics that almost all theorems of countable and countably representable mathematics are equivalent to just five subsystems of second order arithmetic. The standard view is that the significance of these equivalences lies in the set existence principles that are necessary and sufficient to prove those theorems. In this article I analyse the role of set existence principles in reverse mathematics, and argue that they are best understood as closure conditions on the powerset of the natural numbers.

中文翻译：

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设置存在原则和闭包条件：解开逆向数学的标准视图†

逆向数学中的一个惊人事实是，几乎所有可数和可数可表示数学的定理都等价于二阶算术的五个子系统。标准的观点是，这些等价的意义在于证明这些定理的必要和充分的集合存在原则。在本文中，我分析了集合存在原则在逆向数学中的作用，并认为它们最好理解为自然数幂集上的闭包条件。