ABSTRACT

There is no prospect of discovering measurable cardinals by radio astronomy, but this does not mean that higher set theory is entirely irrelevant to applied mathematics broadly construed. By way of example, the bearing of some celebrated descriptive-set-theoretic consequences of large cardinals on measurable-selection theory, a body of results originating with a key lemma in von Neumann’s work on the mathematical foundations of quantum theory, and further developed in connection with problems of mathematical economics, will be considered from a philosophical point of view.

中文翻译：

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可测量的选择：大型基数和科学应用之间的桥梁？†

摘要

没有通过射电天文学发现可测量基数的前景，但这并不意味着更高集理论与广义上的应用数学完全无关。举例来说，大基数对可测量选择理论的一些著名的描述性集合理论结果的影响，一系列结果源于冯诺依曼关于量子理论数学基础的工作中的一个关键引理，并在与数理经济学问题的联系，将从哲学的角度来考虑。