{"title":"超功率公理和GCH","authors":"G. Goldberg","doi":"10.1142/s0219061321500173","DOIUrl":null,"url":null,"abstract":"The Ultrapower Axiom is an abstract combinatorial principle inspired by the fine structure of canonical inner models of large cardinal axioms. In this paper, it is established that the Ultrapower Axiom implies that the Generalized Continuum Hypothesis holds above the least supercompact cardinal.","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":"30 1","pages":"2150017:1-2150017:22"},"PeriodicalIF":0.9000,"publicationDate":"2020-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"The Ultrapower Axiom and the GCH\",\"authors\":\"G. Goldberg\",\"doi\":\"10.1142/s0219061321500173\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Ultrapower Axiom is an abstract combinatorial principle inspired by the fine structure of canonical inner models of large cardinal axioms. In this paper, it is established that the Ultrapower Axiom implies that the Generalized Continuum Hypothesis holds above the least supercompact cardinal.\",\"PeriodicalId\":50144,\"journal\":{\"name\":\"Journal of Mathematical Logic\",\"volume\":\"30 1\",\"pages\":\"2150017:1-2150017:22\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2020-10-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Logic\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s0219061321500173\",\"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/s0219061321500173","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"LOGIC","Score":null,"Total":0}
The Ultrapower Axiom is an abstract combinatorial principle inspired by the fine structure of canonical inner models of large cardinal axioms. In this paper, it is established that the Ultrapower Axiom implies that the Generalized Continuum Hypothesis holds above the least supercompact cardinal.
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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