Computable Structure Theory

奈特和她的学生将研究可计算结构理论的各个方面。奈特计划继续与达阿基诺一起研究薄弱的算术片段。她还希望继续与Goncharov、Harizanov、Young和shore合作，研究一系列相互关联的问题，包括可计算结构、高阶结构和Kleene o的路径上的复杂关系。她目前正在与Csima、Hirschfeldt和Soare合作，研究质数模型和低度性质。她计划与Lempp、McCoy和solomon一起研究布尔代数。这些资金主要用于学生的旅行和书籍。其余部分用于巴黎圣母院逻辑研讨会的部分支持。目前，奈特有两名学生。安德鲁·阿拉纳（Andrew Arana）可能会在今年夏天完成这项研究，他使用了一些新的独立句子（哥德尔-罗瑟句的变体），得出了一些关于算术复杂性的结果。阿拉纳现在正专注于更基本的问题。二年级学生WesleyCalvert正在研究各种熟悉的可计算结构类的同构问题的复杂性。他已经有好几门课的成绩了。在助学金期间，奈特大学可以招收新的学生。奈特和她的学生们的研究目标是确定数学结构的哪些方面是可计算的，而对于那些不可计算的，是否有一些不错的、可计算的近似。这笔拨款将促进这类新工作的开展。有一个更大的目标——让学生成为一流的研究科学家。补助金将主要用于学生的旅行和书本费。如果没有钱买书，奈特的学生几乎不会拥有任何一本书。她发现，如果给钱买最重要的参考资料，她的学生们的阅读量就会大大增加。他们看到他们正在研究的问题是如何产生的，以及他们的工作对整个领域的意义。奈特以前的学生，以及圣母大学其他逻辑专业的学生，都从参加会议的机会中受益匪浅。他们会见来自其他大学的研究人员，并听取最新进展。一旦他们有了自己的结果，他们就会发表演讲，并得到有价值的建议。简而言之，作为学生，他们有机会加入研究型数学家的圈子。

Knight and her students will work on various aspects ofcomputable structure theory. Knight plans to continue work withD'Aquino on weak fragments of arithmetic. She expects also tocontinue work with Goncharov and Harizanov, with Young, and withShore, on a collection of inter-related problems involvingcomplicated relations on computable structures, structures ofhigh rank, and paths through Kleene's O. She is currentlyworking with Csima, Hirschfeldt, and Soare on prime models andlowness properties. She plans to work with Lempp, McCoy, andSolomon on Boolean algebras. The funds are mainly for studenttravel and books. The remainder is for partial support of theNotre Dame Logic Seminar. Currently, Knight has two students.Andrew Arana, who may finish this summer, has a number of resultson complexity in arithmetic, using some new independent sentences(variants of the Godel-Rosser sentence). Arana is nowconcentrating on problems of a more foundational nature. WesleyCalvert, a second year student, is working on complexity of theisomorphism problem for various familiar classes of computablestructures. He already has results for several classes offields. Knight may acquire new students during the period of thegrant.The goal of Knight's research, and that of students working withher, is to determine which aspects of mathematical structures arecomputable, and for those which are not computable, whether thereis some nice, computable approximation. The grant willfacilitate new work of this kind. There is a largergoal---enabling students to become first-rate researchscientists. The grant will be used mainly for student travel andbooks. Without money for books, Knight's students would hardlyown any. She has found that, given money to buy the mostimportant references, her students read much more than they wouldotherwise. They see how the problems they are working on arose,and what their work means for the field as a whole. Knight'spast students, and other logic students at Notre Dame, havebenefited tremendously from opportunities to travel to meetings.They meet researchers from other universities and hear about newdevelopments. As soon as they have results of their own, theygive talks, and they get valuable suggestions. In short, theyhave the opportunity, as students, to join the community ofresearch mathematicians.