This paper is the second in a series of three culminating in an ordinal analysis of 2-comprehension. Its objective is to present an ordinal analysis for the subsystem of second order arithmetic with 2-comprehension, bar induction and 1 2-comprehension for formulae without set parameters. Couched in terms of Kripke-Platek set theory, KP, the latter system corresponds to KPi augmented by the assertion that there exists a stable ordinal, where KPi is KP with an additional axiom stating that every set is contained in an admissible set.
{"title":"Mathematical Logic","authors":"I. Jebril, H. Dutta, Ilwoo Cho","doi":"10.1201/9780429022838-1","DOIUrl":"https://doi.org/10.1201/9780429022838-1","url":null,"abstract":"This paper is the second in a series of three culminating in an ordinal analysis of 2-comprehension. Its objective is to present an ordinal analysis for the subsystem of second order arithmetic with 2-comprehension, bar induction and 1 2-comprehension for formulae without set parameters. Couched in terms of Kripke-Platek set theory, KP, the latter system corresponds to KPi augmented by the assertion that there exists a stable ordinal, where KPi is KP with an additional axiom stating that every set is contained in an admissible set.","PeriodicalId":231325,"journal":{"name":"Concise Introduction to Logic and Set Theory","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125696192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Cardinality of Sets","authors":"I. Jebril, H. Dutta, Ilwoo Cho","doi":"10.1201/9780429022838-5","DOIUrl":"https://doi.org/10.1201/9780429022838-5","url":null,"abstract":"","PeriodicalId":231325,"journal":{"name":"Concise Introduction to Logic and Set Theory","volume":"210 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133929346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Relations","authors":"Iqbal H. Jebril, H. Dutta, Ilwoo Cho","doi":"10.1201/9780429022838-3","DOIUrl":"https://doi.org/10.1201/9780429022838-3","url":null,"abstract":"","PeriodicalId":231325,"journal":{"name":"Concise Introduction to Logic and Set Theory","volume":"143 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124716086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Set Theory","authors":"Iqbal H. Jebril, Hemen Dutta, Ilwoo Cho","doi":"10.1201/9780429022838-2","DOIUrl":"https://doi.org/10.1201/9780429022838-2","url":null,"abstract":"","PeriodicalId":231325,"journal":{"name":"Concise Introduction to Logic and Set Theory","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122187284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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