Jörg Brendle , Lorenz J. Halbeisen , Lukas Daniel Klausner , Marc Lischka , Saharon Shelah
{"title":"半新基本特征","authors":"Jörg Brendle , Lorenz J. Halbeisen , Lukas Daniel Klausner , Marc Lischka , Saharon Shelah","doi":"10.1016/j.apal.2023.103303","DOIUrl":null,"url":null,"abstract":"<div><p>Based on the well-known cardinal characteristics <span><math><mi>s</mi></math></span>, <span><math><mi>r</mi></math></span> and <span><math><mi>i</mi></math></span>, we introduce nine related cardinal characteristics by using the notion of asymptotic density to characterise different intersection properties of infinite sets. We prove several bounds and consistency results, e.g. the consistency of <span><math><mi>s</mi><mo><</mo><msub><mrow><mi>s</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msub></math></span>, as well as several results about possible values of <span><math><msub><mrow><mi>i</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msub></math></span>.</p></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"174 9","pages":"Article 103303"},"PeriodicalIF":0.6000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Halfway new cardinal characteristics\",\"authors\":\"Jörg Brendle , Lorenz J. Halbeisen , Lukas Daniel Klausner , Marc Lischka , Saharon Shelah\",\"doi\":\"10.1016/j.apal.2023.103303\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Based on the well-known cardinal characteristics <span><math><mi>s</mi></math></span>, <span><math><mi>r</mi></math></span> and <span><math><mi>i</mi></math></span>, we introduce nine related cardinal characteristics by using the notion of asymptotic density to characterise different intersection properties of infinite sets. We prove several bounds and consistency results, e.g. the consistency of <span><math><mi>s</mi><mo><</mo><msub><mrow><mi>s</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msub></math></span>, as well as several results about possible values of <span><math><msub><mrow><mi>i</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msub></math></span>.</p></div>\",\"PeriodicalId\":50762,\"journal\":{\"name\":\"Annals of Pure and Applied Logic\",\"volume\":\"174 9\",\"pages\":\"Article 103303\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Pure and Applied Logic\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S016800722300060X\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"LOGIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Pure and Applied Logic","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S016800722300060X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"LOGIC","Score":null,"Total":0}
Based on the well-known cardinal characteristics , and , we introduce nine related cardinal characteristics by using the notion of asymptotic density to characterise different intersection properties of infinite sets. We prove several bounds and consistency results, e.g. the consistency of , as well as several results about possible values of .
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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