{"title":"Cardinal characteristics on bounded generalised Baire spaces","authors":"Tristan van der Vlugt","doi":"10.1016/j.apal.2025.103582","DOIUrl":null,"url":null,"abstract":"<div><div>We will give an overview of four families of cardinal characteristics defined on subspaces <span><math><msub><mrow><mo>∏</mo></mrow><mrow><mi>α</mi><mo>∈</mo><mi>κ</mi></mrow></msub><mi>b</mi><mo>(</mo><mi>α</mi><mo>)</mo></math></span> of the generalised Baire space <span><math><mmultiscripts><mrow><mi>κ</mi></mrow><mprescripts></mprescripts><none></none><mrow><mi>κ</mi></mrow></mmultiscripts></math></span>, where <em>κ</em> is strongly inaccessible and <span><math><mi>b</mi><mo>∈</mo><msup><mrow></mrow><mrow><mi>κ</mi></mrow></msup><mi>κ</mi></math></span>. The considered families are bounded versions of the dominating, eventual difference, localisation and antilocalisation numbers, and their dual cardinals. We investigate parameters for which these cardinals are nontrivial and how the cardinals relate to each other and to other cardinals of the generalised Cichoń diagram. Finally we prove that different choices of parameters may lead to consistently distinct cardinals.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 7","pages":"Article 103582"},"PeriodicalIF":0.6000,"publicationDate":"2025-03-12","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/S0168007225000314","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
We will give an overview of four families of cardinal characteristics defined on subspaces of the generalised Baire space , where κ is strongly inaccessible and . The considered families are bounded versions of the dominating, eventual difference, localisation and antilocalisation numbers, and their dual cardinals. We investigate parameters for which these cardinals are nontrivial and how the cardinals relate to each other and to other cardinals of the generalised Cichoń diagram. Finally we prove that different choices of parameters may lead to consistently distinct cardinals.
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.