{"title":"Social welfare relations and irregular sets","authors":"Ram Sewak Dubey , Giorgio Laguzzi","doi":"10.1016/j.apal.2023.103302","DOIUrl":null,"url":null,"abstract":"<div><p>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 <span>[4, Problem 11.14]</span>, 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 <em>social welfare diagram</em> 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.</p></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"174 9","pages":"Article 103302"},"PeriodicalIF":0.6000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Pure and Applied Logic","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0168007223000593","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"LOGIC","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍：
The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.
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