{"title":"在Presburger群中，可定义的设置为可定义的双反","authors":"R. Cluckers, Immanuel Halupczok","doi":"10.1112/tlm3.12011","DOIUrl":null,"url":null,"abstract":"We entirely classify definable sets up to definable bijections in Z ‐groups, where the language is the one of ordered abelian groups. From this, we deduce, among others, a classification of definable families of bounded definable sets.","PeriodicalId":41208,"journal":{"name":"Transactions of the London Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2017-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1112/tlm3.12011","citationCount":"2","resultStr":"{\"title\":\"Definable sets up to definable bijections in Presburger groups\",\"authors\":\"R. Cluckers, Immanuel Halupczok\",\"doi\":\"10.1112/tlm3.12011\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We entirely classify definable sets up to definable bijections in Z ‐groups, where the language is the one of ordered abelian groups. From this, we deduce, among others, a classification of definable families of bounded definable sets.\",\"PeriodicalId\":41208,\"journal\":{\"name\":\"Transactions of the London Mathematical Society\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2017-06-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1112/tlm3.12011\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions of the London Mathematical Society\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1112/tlm3.12011\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of the London Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1112/tlm3.12011","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Definable sets up to definable bijections in Presburger groups
We entirely classify definable sets up to definable bijections in Z ‐groups, where the language is the one of ordered abelian groups. From this, we deduce, among others, a classification of definable families of bounded definable sets.
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