Social welfare relations and irregular sets

Ram Sewak Dubey, Giorgio Laguzzi

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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.

Lingua originaleInglese
Numero di articolo103302
RivistaAnnals of Pure and Applied Logic
Volume174
Numero di pubblicazione9
DOI
Stato di pubblicazionePubblicato - 1 ott 2023

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