论无需选择公理的强公平社会福利序
On Strongly-equitable Social Welfare Orders Without the Axiom of Choice
AI总结：
本文研究强公平且有限匿名的社会福利序（SEA），证明其存在蕴含不可勒贝格测度的实数集存在，但不蕴含自然数上非主超滤子的存在，并运用几何集合论技术解决开放问题。
摘要：
社会福利序旨在以某种合理公平的方式，将无限代际的迥异偏好合并为单一的社会偏好序。在文献[2]中，Dubey和Laguzzi研究了一种他们称为SEA的社会福利序类型，即强公平且（有限）匿名的社会福利序。他们证明了SEA序的存在蕴含一个不具有贝尔性质（Baire property）的实数集的存在，并指出$\u2115$上的非主超滤子可用于构造SEA序。他们工作中提出的问题包括：SEA序的存在是否蕴含一个不可勒贝格测度（Lebesgue-measurable）的实数集的存在，或$\u2115$上的非主超滤子的存在。我们回答了这两个问题，其中第二个问题的解答使用了Larson和Zapletal在文献[11]中阐述的几何集合论技术。结果是：SEA序的存在确实蕴含一个不可勒贝格测度的实数集的存在，但不蕴含$\u2115$上非主超滤子的存在。
英文摘要：
Social welfare orders seek to combine the disparate preferences of an infinite sequence of generations into a single, societal preference order in some reasonably-equitable way. In [2] Dubey and Laguzzi study a type of social welfare order which they call SEA, for strongly equitable and (finitely) anonymous. They prove that the existence of a SEA order implies the existence of a set of reals which does not have the Baire property, and observe that a nonprincipal ultrafilter over $\mathbb{N}$ can be used to construct a SEA order. Questions arising in their work include whether the existence of a SEA order implies the existence of either a set of real numbers which is not Lebesgue-measurable or of a nonprincipal ultrafilter over $\mathbb{N}$. We answer both these questions, the solution to the second using the techniques of geometric set theory as set out by Larson and Zapletal in [11]. The outcome is that the existence of a SEA order does imply the existence of a set of reals which is not Lebesgue-measurable, and does not imply the existence of a nonprincipal ultrafilter on $\mathbb{N}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
