{"title":"隐含格和Heyting代数的无选择拓扑对偶性","authors":"Chrysafis Hartonas","doi":"10.1007/s00012-023-00830-8","DOIUrl":null,"url":null,"abstract":"<div><p>We develop a common semantic framework for the interpretation both of <span>\\({\\textbf {IPC}}\\)</span>, the intuitionistic propositional calculus, and of logics weaker than <span>\\({\\textbf {IPC}}\\)</span> (substructural and subintuitionistic logics). To this end, we prove a choice-free representation and duality theorem for implicative lattices, which may or may not be distributive. The duality specializes to a choice-free duality for the full subcategory of Heyting algebras and a category of topological sorted frames with a ternary sorted relation.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"85 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Choice-free topological duality for implicative lattices and Heyting algebras\",\"authors\":\"Chrysafis Hartonas\",\"doi\":\"10.1007/s00012-023-00830-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We develop a common semantic framework for the interpretation both of <span>\\\\({\\\\textbf {IPC}}\\\\)</span>, the intuitionistic propositional calculus, and of logics weaker than <span>\\\\({\\\\textbf {IPC}}\\\\)</span> (substructural and subintuitionistic logics). To this end, we prove a choice-free representation and duality theorem for implicative lattices, which may or may not be distributive. The duality specializes to a choice-free duality for the full subcategory of Heyting algebras and a category of topological sorted frames with a ternary sorted relation.</p></div>\",\"PeriodicalId\":50827,\"journal\":{\"name\":\"Algebra Universalis\",\"volume\":\"85 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-11-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebra Universalis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00012-023-00830-8\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra Universalis","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00012-023-00830-8","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Choice-free topological duality for implicative lattices and Heyting algebras
We develop a common semantic framework for the interpretation both of \({\textbf {IPC}}\), the intuitionistic propositional calculus, and of logics weaker than \({\textbf {IPC}}\) (substructural and subintuitionistic logics). To this end, we prove a choice-free representation and duality theorem for implicative lattices, which may or may not be distributive. The duality specializes to a choice-free duality for the full subcategory of Heyting algebras and a category of topological sorted frames with a ternary sorted relation.
期刊介绍:
Algebra Universalis publishes papers in universal algebra, lattice theory, and related fields. In a pragmatic way, one could define the areas of interest of the journal as the union of the areas of interest of the members of the Editorial Board. In addition to research papers, we are also interested in publishing high quality survey articles.