{"title":"关于域中存在不可判性的两个例子","authors":"PHILIP DITTMANN","doi":"10.1017/jsl.2023.87","DOIUrl":null,"url":null,"abstract":"<p>We construct an existentially undecidable complete discretely valued field of mixed characteristic with existentially decidable residue field and decidable algebraic part, answering a question by Anscombe–Fehm in a strong way. Along the way, we construct an existentially decidable field of positive characteristic with an existentially undecidable finite extension, modifying a construction due to Kesavan Thanagopal.</p>","PeriodicalId":501300,"journal":{"name":"The Journal of Symbolic Logic","volume":"164 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"TWO EXAMPLES CONCERNING EXISTENTIAL UNDECIDABILITY IN FIELDS\",\"authors\":\"PHILIP DITTMANN\",\"doi\":\"10.1017/jsl.2023.87\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We construct an existentially undecidable complete discretely valued field of mixed characteristic with existentially decidable residue field and decidable algebraic part, answering a question by Anscombe–Fehm in a strong way. Along the way, we construct an existentially decidable field of positive characteristic with an existentially undecidable finite extension, modifying a construction due to Kesavan Thanagopal.</p>\",\"PeriodicalId\":501300,\"journal\":{\"name\":\"The Journal of Symbolic Logic\",\"volume\":\"164 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-11-23\",\"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.2023.87\",\"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.2023.87","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
TWO EXAMPLES CONCERNING EXISTENTIAL UNDECIDABILITY IN FIELDS
We construct an existentially undecidable complete discretely valued field of mixed characteristic with existentially decidable residue field and decidable algebraic part, answering a question by Anscombe–Fehm in a strong way. Along the way, we construct an existentially decidable field of positive characteristic with an existentially undecidable finite extension, modifying a construction due to Kesavan Thanagopal.
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
