{"title":"模型理论Elekes-Szabó在强极小情况下","authors":"A. Chernikov, S. Starchenko","doi":"10.1142/S0219061321500045","DOIUrl":null,"url":null,"abstract":"We prove a generalization of the Elekes–Szabó theorem [G. Elekes and E. Szabó, How to find groups? (and how to use them in Erdos geometry?), Combinatorica 32(5) 537–571 (2012)] for relations definable in strongly minimal structures that are interpretable in distal structures.","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":"17 1","pages":"2150004:1-2150004:20"},"PeriodicalIF":0.9000,"publicationDate":"2020-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"Model-theoretic Elekes-Szabó in the strongly minimal case\",\"authors\":\"A. Chernikov, S. Starchenko\",\"doi\":\"10.1142/S0219061321500045\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove a generalization of the Elekes–Szabó theorem [G. Elekes and E. Szabó, How to find groups? (and how to use them in Erdos geometry?), Combinatorica 32(5) 537–571 (2012)] for relations definable in strongly minimal structures that are interpretable in distal structures.\",\"PeriodicalId\":50144,\"journal\":{\"name\":\"Journal of Mathematical Logic\",\"volume\":\"17 1\",\"pages\":\"2150004:1-2150004:20\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2020-10-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Logic\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/S0219061321500045\",\"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/S0219061321500045","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"LOGIC","Score":null,"Total":0}
Model-theoretic Elekes-Szabó in the strongly minimal case
We prove a generalization of the Elekes–Szabó theorem [G. Elekes and E. Szabó, How to find groups? (and how to use them in Erdos geometry?), Combinatorica 32(5) 537–571 (2012)] for relations definable in strongly minimal structures that are interpretable in distal structures.
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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