{"title":"超稳定场和群","authors":"G. Cherlin , S. Shelah","doi":"10.1016/0003-4843(80)90006-6","DOIUrl":null,"url":null,"abstract":"<div><p>We prove an indecomposability theorem for connected stable groups. Using this theorem we prove that all infinite superstable fields are algebraically closed, and we extend known results for ω-stable groups of Morley rank at most 3 to the corresponding class of superstable groups (Note: The logical notion of stability is unrelated to the notion of stability in finit group theory).</p></div>","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"18 3","pages":"Pages 227-270"},"PeriodicalIF":0.0000,"publicationDate":"1980-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0003-4843(80)90006-6","citationCount":"81","resultStr":"{\"title\":\"Superstable fields and groups\",\"authors\":\"G. Cherlin , S. Shelah\",\"doi\":\"10.1016/0003-4843(80)90006-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We prove an indecomposability theorem for connected stable groups. Using this theorem we prove that all infinite superstable fields are algebraically closed, and we extend known results for ω-stable groups of Morley rank at most 3 to the corresponding class of superstable groups (Note: The logical notion of stability is unrelated to the notion of stability in finit group theory).</p></div>\",\"PeriodicalId\":100093,\"journal\":{\"name\":\"Annals of Mathematical Logic\",\"volume\":\"18 3\",\"pages\":\"Pages 227-270\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1980-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/0003-4843(80)90006-6\",\"citationCount\":\"81\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Mathematical Logic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/0003484380900066\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Mathematical Logic","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/0003484380900066","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We prove an indecomposability theorem for connected stable groups. Using this theorem we prove that all infinite superstable fields are algebraically closed, and we extend known results for ω-stable groups of Morley rank at most 3 to the corresponding class of superstable groups (Note: The logical notion of stability is unrelated to the notion of stability in finit group theory).
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