{"title":"非极小性的程度最多为2","authors":"J. Freitag, Rémi Jaoui, Rahim Moosa","doi":"10.1142/S0219061322500313","DOIUrl":null,"url":null,"abstract":". It is shown that if p ∈ S ( A ) is a complete type of Lascar rank at least 2, in the theory of differentially closed fields of characteristic zero, then there exists a pair of realisations a 1 ,a 2 such that p has a nonalgebraic forking extension over Aa 1 a 2 . Moreover, if A is contained in the field of constants then p already has a nonalgebraic forking extension over Aa 1 . The results are also formulated in a more general setting.","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":"26 1","pages":"2250031:1-2250031:6"},"PeriodicalIF":0.9000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"The degree of nonminimality is at most 2\",\"authors\":\"J. Freitag, Rémi Jaoui, Rahim Moosa\",\"doi\":\"10.1142/S0219061322500313\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". It is shown that if p ∈ S ( A ) is a complete type of Lascar rank at least 2, in the theory of differentially closed fields of characteristic zero, then there exists a pair of realisations a 1 ,a 2 such that p has a nonalgebraic forking extension over Aa 1 a 2 . Moreover, if A is contained in the field of constants then p already has a nonalgebraic forking extension over Aa 1 . The results are also formulated in a more general setting.\",\"PeriodicalId\":50144,\"journal\":{\"name\":\"Journal of Mathematical Logic\",\"volume\":\"26 1\",\"pages\":\"2250031:1-2250031:6\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Logic\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/S0219061322500313\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"LOGIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Logic","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/S0219061322500313","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"LOGIC","Score":null,"Total":0}
引用次数: 2
摘要
． 证明了在特征为0的微分闭域理论中，如果p∈S (A)是至少为2的完备型Lascar秩，则存在一对实现A 1, A 2，使得p在A 1 A 2上具有非代数分叉扩展。此外，如果A包含在常数域中，则p在aa1上已经具有非代数分叉扩展。结果也在更一般的情况下制定。
. It is shown that if p ∈ S ( A ) is a complete type of Lascar rank at least 2, in the theory of differentially closed fields of characteristic zero, then there exists a pair of realisations a 1 ,a 2 such that p has a nonalgebraic forking extension over Aa 1 a 2 . Moreover, if A is contained in the field of constants then p already has a nonalgebraic forking extension over Aa 1 . The results are also formulated in a more general setting.
期刊介绍：
The Journal of Mathematical Logic (JML) provides an important forum for the communication of original contributions in all areas of mathematical logic and its applications. It aims at publishing papers at the highest level of mathematical creativity and sophistication. JML intends to represent the most important and innovative developments in the subject.
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