{"title":"几何结构的超级性和密集对","authors":"Gareth J. Boxall","doi":"10.1007/s00153-023-00890-6","DOIUrl":null,"url":null,"abstract":"<div><p>Let <i>T</i> be a complete geometric theory and let <span>\\(T_P\\)</span> be the theory of dense pairs of models of <i>T</i>. We show that if <i>T</i> is superrosy with <img>-rank 1 then <span>\\(T_P\\)</span> is superrosy with <img>-rank at most <span>\\(\\omega \\)</span>.\n</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-023-00890-6.pdf","citationCount":"0","resultStr":"{\"title\":\"Superrosiness and dense pairs of geometric structures\",\"authors\":\"Gareth J. Boxall\",\"doi\":\"10.1007/s00153-023-00890-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Let <i>T</i> be a complete geometric theory and let <span>\\\\(T_P\\\\)</span> be the theory of dense pairs of models of <i>T</i>. We show that if <i>T</i> is superrosy with <img>-rank 1 then <span>\\\\(T_P\\\\)</span> is superrosy with <img>-rank at most <span>\\\\(\\\\omega \\\\)</span>.\\n</p></div>\",\"PeriodicalId\":48853,\"journal\":{\"name\":\"Archive for Mathematical Logic\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-09-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s00153-023-00890-6.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Archive for Mathematical Logic\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00153-023-00890-6\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Arts and Humanities\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive for Mathematical Logic","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00153-023-00890-6","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Arts and Humanities","Score":null,"Total":0}
Superrosiness and dense pairs of geometric structures
Let T be a complete geometric theory and let \(T_P\) be the theory of dense pairs of models of T. We show that if T is superrosy with -rank 1 then \(T_P\) is superrosy with -rank at most \(\omega \).
期刊介绍：
The journal publishes research papers and occasionally surveys or expositions on mathematical logic. Contributions are also welcomed from other related areas, such as theoretical computer science or philosophy, as long as the methods of mathematical logic play a significant role. The journal therefore addresses logicians and mathematicians, computer scientists, and philosophers who are interested in the applications of mathematical logic in their own field, as well as its interactions with other areas of research.
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