Indestructibility Phenomena of Large Cardinals

99709993哈姆金斯教授将继续他对大型枢机的不可破坏现象的研究。这项工作是两大集合理论研究工作的共同焦点，即强迫和大基数，鉴于他早期在间隙强迫和彩票准备方面的工作最近取得的进展，这项工作似乎特别有希望。具体来说，哈姆金斯教授将研究一系列悬而未决的问题，这些问题涉及各种大型枢机在多大程度上可能具有不可摧毁性，并特别关注强紧凑枢机。除了这项工作，他还将继续他的另外两个项目，自同构塔问题和无限时间图灵机的新理论，无限计算模型。哈姆金斯教授的研究涉及到崇高的、难以理解的数学无穷大概念的研究，这个概念几个世纪以来一直吸引着数学家。在二十世纪，特别是在过去的三十年里，集合理论家已经对这些超限数中最大的一个——大基数——有了深刻的理解。哈姆金斯教授对大基数如何受到强迫的影响特别感兴趣，强迫是保罗·科恩（Paul Cohen）发明的一种技术，通过这种技术，集合论者得以瞥见不同的数学宇宙，并意识到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工作上，即强迫和大基数。他将努力研究这些基数的奇特的不可摧毁性现象，通过这种现象，它们的巨大存在于各种各样的数学宇宙中。* * *

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. ***