{"title":"间隔数","authors":"IVO DÜNTSCH, RAFAŁ GRUSZCZYŃSKI, PAULA MENCHÓN","doi":"10.1017/jsl.2023.86","DOIUrl":null,"url":null,"abstract":"We introduce and study a class of <jats:italic>betweenness algebras</jats:italic>—Boolean algebras with binary operators, closely related to ternary frames with a betweenness relation. From various axioms for betweenness, we chose those that are most common, which makes our work applicable to a wide range of betweenness structures studied in the literature. On the algebraic side, we work with two operators of <jats:italic>possibility</jats:italic> and of <jats:italic>sufficiency</jats:italic>.","PeriodicalId":501300,"journal":{"name":"The Journal of Symbolic Logic","volume":"208 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"BETWEENNESS ALGEBRAS\",\"authors\":\"IVO DÜNTSCH, RAFAŁ GRUSZCZYŃSKI, PAULA MENCHÓN\",\"doi\":\"10.1017/jsl.2023.86\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce and study a class of <jats:italic>betweenness algebras</jats:italic>—Boolean algebras with binary operators, closely related to ternary frames with a betweenness relation. From various axioms for betweenness, we chose those that are most common, which makes our work applicable to a wide range of betweenness structures studied in the literature. On the algebraic side, we work with two operators of <jats:italic>possibility</jats:italic> and of <jats:italic>sufficiency</jats:italic>.\",\"PeriodicalId\":501300,\"journal\":{\"name\":\"The Journal of Symbolic Logic\",\"volume\":\"208 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-02-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Journal of Symbolic Logic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/jsl.2023.86\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Journal of Symbolic Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/jsl.2023.86","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We introduce and study a class of betweenness algebras—Boolean algebras with binary operators, closely related to ternary frames with a betweenness relation. From various axioms for betweenness, we chose those that are most common, which makes our work applicable to a wide range of betweenness structures studied in the literature. On the algebraic side, we work with two operators of possibility and of sufficiency.
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