Mathematical Sciences: Recursive Model Theory

数学科学：递归模型理论

• 批准号: 8701559
• 负责人: Julia Knight
• 金额: $ 9.06万
• 依托单位: University of Notre Dame
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-06-15 至 1990-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701559&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Recursive; Model; Theory

Knight is continuing her work in recursive model theory. Over the past two years, she has obtained several results on degrees of models realizing prescribed sets of bounded complexity types (finitary or infinitary). The problem of characterizing the degrees of isomorphic copies of a given model now seems approachable. Knight and Slaman have a characterization for models of finite Scott height. The characterization is unpleasantly complicated, and they hope to simplify it. The recent results use a powerful method of Harrington. In addition to using the method to obtain further results, Knight hopes to come to a better understanding of the method itself. Ash developed a related method and proved a theorem giving general conditions under which his method works. Ash and Knight have begun trying to compare the two methods. All of these investigations shed further light on the theoretical limits of computing power, a matter that becomes increasingly relevant and fascinating as the actual limits of computing power expand with each generation of new machines.

奈特正在继续她在递归模型理论方面的工作。在过去的两年里，她得到了几个关于模型实现规定的有界复杂性类型(有限或无限)集的次数的结果。刻画给定模型的同构副本的次数的问题现在似乎是可以接近的。奈特和斯拉曼对有限斯科特身高的模型有一个刻画。人物塑造复杂得令人不快，他们希望将其简单化。最近的结果使用了哈林顿的一种强有力的方法。除了使用该方法获得进一步的结果外，奈特还希望对该方法本身有更好的了解。Ash发展了一种相关的方法，并证明了一个定理，给出了他的方法适用的一般条件。阿什和奈特已经开始尝试比较这两种方法。所有这些调查都进一步揭示了计算能力的理论极限，随着计算能力的实际极限随着每一代新机器的扩大，这个问题变得越来越相关和有趣。