{"title":"Lattice Ordered O-Minimal Structures","authors":"C. Toffalori","doi":"10.1305/ndjfl/1039118862","DOIUrl":null,"url":null,"abstract":"We propose a notion of o -minimality for partially ordered structures. Then we study o -minimal partially ordered structures ( A , ≤ , . . .) such that ( A , ≤ ) is a Boolean algebra. We prove that they admit prime models over arbitrary subsets and we characterize ω -categoricity in their setting. Finally, we classify o -minimal Boolean algebras as well as o -minimal measure spaces.","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":"7 1","pages":"447-463"},"PeriodicalIF":0.5000,"publicationDate":"1998-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"15","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Notre Dame Journal of Formal Logic","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1305/ndjfl/1039118862","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"LOGIC","Score":null,"Total":0}
引用次数: 15
Abstract
We propose a notion of o -minimality for partially ordered structures. Then we study o -minimal partially ordered structures ( A , ≤ , . . .) such that ( A , ≤ ) is a Boolean algebra. We prove that they admit prime models over arbitrary subsets and we characterize ω -categoricity in their setting. Finally, we classify o -minimal Boolean algebras as well as o -minimal measure spaces.
期刊介绍：
The Notre Dame Journal of Formal Logic, founded in 1960, aims to publish high quality and original research papers in philosophical logic, mathematical logic, and related areas, including papers of compelling historical interest. The Journal is also willing to selectively publish expository articles on important current topics of interest as well as book reviews.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
