Download This PaperSocial welfare relations and irregular sets
Annals of Pure and Applied Logic, Volume 174, Issue 9, 2023 103302, ISSN 0168-0072, https://doi.org/10.1016/j.apal.2023.103302. (https://www.sciencedirect.com/science/article/pii/S0168007223000593)
17 Pages Posted: 8 Nov 2019 Last revised: 26 Apr 2024
Date Written: April 26, 2024
Abstract
Social welfare relations satisfying Pareto and equity principles on infinite utility streams have revealed a non-constructive nature, specifically by showing that in general they imply the existence of non-Ramsey sets and non-Lebesgue measurable sets. In [4, Problem 11.14], the authors ask whether such a connection holds with non-Baire sets as well. In this paper we answer such a question showing that several versions of Pareto principles acting on different utility domains imply the existence of non-Baire sets. Furthermore, we analyze in more details the needed fragments of AC and we start a systematic investigation of a social welfare diagram in a similar fashion done in the past decades concerning cardinal invariants and regularity properties of the reals. In doing that we use tools from forcing theory, such as specific tree-forcings (in particular variants of Silver and Mathias forcings) and Shelah's amalgamation.
Keywords: Forcing; Descriptive set theory; Social welfare relations; Infinite utility streams
JEL Classification: D60, D70, D90.
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