{"title":"相当或极小理论的非本质扩展","authors":"B. Sh. Kulpeshov, S. V. Sudoplatov","doi":"10.1134/s1995080224600687","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We study constant expansions of quite o-minimal theories. We prove that any non-essential expansion (expansion by finitely many new constants) of a quite o-minimal Ehrenfeucht theory of finite convexity rank preserves Ehrenfeuchtness. We also establish that the countable spectrum of such an expanded theory is not decreased.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"64 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Non-Essential Expansions of Quite o-Minimal Theories\",\"authors\":\"B. Sh. Kulpeshov, S. V. Sudoplatov\",\"doi\":\"10.1134/s1995080224600687\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p>We study constant expansions of quite o-minimal theories. We prove that any non-essential expansion (expansion by finitely many new constants) of a quite o-minimal Ehrenfeucht theory of finite convexity rank preserves Ehrenfeuchtness. We also establish that the countable spectrum of such an expanded theory is not decreased.</p>\",\"PeriodicalId\":46135,\"journal\":{\"name\":\"Lobachevskii Journal of Mathematics\",\"volume\":\"64 1\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-07-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Lobachevskii Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1134/s1995080224600687\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lobachevskii Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1995080224600687","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
摘要 我们研究相当 O 最小理论的常数展开。我们证明了有限凸性阶的相当 O 最小艾伦福赫特理论的任何非本质扩展（由有限多个新常数进行的扩展）都保留了艾伦福赫特性。我们还证明了这种扩展理论的可数谱不会减少。
Non-Essential Expansions of Quite o-Minimal Theories
Abstract
We study constant expansions of quite o-minimal theories. We prove that any non-essential expansion (expansion by finitely many new constants) of a quite o-minimal Ehrenfeucht theory of finite convexity rank preserves Ehrenfeuchtness. We also establish that the countable spectrum of such an expanded theory is not decreased.
期刊介绍：
Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.
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