Indestructibility Phenomena of Large Cardinals

大红衣主教的坚不可摧现象

• 批准号: 9970993
• 负责人: Joel Hamkins
• 金额: $ 7.44万
• 依托单位: Research Foundation of the City University of New York
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-07-15 至 2003-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9970993&HistoricalAwards=false
• 关键词: Indestructibility; Phenomena; Large; Cardinals

9970993Hamkins Professor Hamkins will continue his research on the indestructibility phenomena of large cardinals. This work, lying at the common focus of twobroad set-theoretic research efforts, namely, forcing and large cardinals,seems particularly promising in light of the recent advances that haveemerged from his earlier work with gap forcing and the lottery preparation.Specifically, Professor Hamkins will investigate a series of open questionsconcerning the extent to which indestructibility is possible with variouskinds of large cardinals, with a particular focus on the strongly compactcardinals. In addition to this work, he will continue his work on two otherprojects, the automorphism tower problem and the new theory of infinite timeTuring machines, a model of infinitary computation. Professor Hamkins' research involves the study of the sublime, inaccessible notions of mathematical infinity, which have fascinated mathematicians for centuries. In the twentieth century, particularly in the past thirty years, set theorists have gained a profound understandingof the largest of these transfinite numbers, large cardinals. ProfessorHamkins has been particularly interested in how large cardinals areaffected by forcing, the technique invented by Paul Cohen by which settheorists have had glimpses into alternative mathematical universes andrealized the rich diversity of mathematical possibility. Much of his worktherefore lies in the common focus of two major set-theoretic researchefforts, namely, forcing and large cardinals. He will endeavor toinvestigate the curious indestructibility phenomena of these cardinals, bywhich their largeness survives in a wide variety of mathematical universes. ***

小行星9970993 哈姆金斯教授将继续他对大红雀的不灭现象的研究。 这项工作，躺在两个broad集理论的研究工作，即共同的焦点，迫使和大型基数，似乎特别有前途的光，最近的进展，已经出现了从他的早期工作与差距迫使和彩票准备。具体而言，教授Hamkins将调查一系列悬而未决的问题，在何种程度上不灭性是可能的各种大型基数，with a particular特定focus焦点on the strongly强compactcardinals紧cardinals枢机主教. 除了这项工作，他将继续他的工作对两个otherprojects，自同构塔问题和新理论的无限时间图灵机，模型的无限计算。 哈姆金斯教授的研究涉及到数学无穷大的崇高的、难以理解的概念，这些概念几个世纪以来一直吸引着数学家。 在20世纪，特别是在过去的30年里，集合理论家已经对这些超限数中最大的一个，即大基数，有了深刻的理解。 Hamkins教授一直特别感兴趣的是大基数如何受到强迫的影响，这是Paul Cohen发明的一种技术，集合理论家通过这种技术瞥见了替代的数学宇宙，并实现了数学可能性的丰富多样性。 因此，他的大部分工作都集中在两个主要的集合论研究成果中，即强迫和大基数。 他将奋进调查这些红衣主教的奇怪的不灭现象，他们的大生存在各种各样的数学宇宙。 ***