{"title":"相对化操作集理论","authors":"Gerhard Jäger","doi":"10.1017/BSL.2016.11","DOIUrl":null,"url":null,"abstract":"We introduce a way of relativizing operational set theory that also takes care of application. After presenting the basic approach and proving some essential properties of this new form of relativization we turn to the notion of relativized regularity and to the system OST (LR) that extends OST by a limit axiom claiming that any set is element of a relativized regular set. Finally we show that OST (LR) is proof-theoretically equivalent to the well-known theory KPi for a recursively inaccessible universe.","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/BSL.2016.11","citationCount":"2","resultStr":"{\"title\":\"Relativizing Operational Set Theory\",\"authors\":\"Gerhard Jäger\",\"doi\":\"10.1017/BSL.2016.11\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce a way of relativizing operational set theory that also takes care of application. After presenting the basic approach and proving some essential properties of this new form of relativization we turn to the notion of relativized regularity and to the system OST (LR) that extends OST by a limit axiom claiming that any set is element of a relativized regular set. Finally we show that OST (LR) is proof-theoretically equivalent to the well-known theory KPi for a recursively inaccessible universe.\",\"PeriodicalId\":55307,\"journal\":{\"name\":\"Bulletin of Symbolic Logic\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2016-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1017/BSL.2016.11\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of Symbolic Logic\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/BSL.2016.11\",\"RegionNum\":3,\"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":"Bulletin of Symbolic Logic","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/BSL.2016.11","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"LOGIC","Score":null,"Total":0}
We introduce a way of relativizing operational set theory that also takes care of application. After presenting the basic approach and proving some essential properties of this new form of relativization we turn to the notion of relativized regularity and to the system OST (LR) that extends OST by a limit axiom claiming that any set is element of a relativized regular set. Finally we show that OST (LR) is proof-theoretically equivalent to the well-known theory KPi for a recursively inaccessible universe.
期刊介绍：
The Bulletin of Symbolic Logic was established in 1995 by the Association for Symbolic Logic to provide a journal of high standards that would be both accessible and of interest to as wide an audience as possible. It is designed to cover all areas within the purview of the ASL: mathematical logic and its applications, philosophical and non-classical logic and its applications, history and philosophy of logic, and philosophy and methodology of mathematics.
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