Mathematical Sciences: Recursive Model Theory

奈特继续她在递归模型理论方面的工作。 在过去的两年里，她已经取得了一些成果， 模型实现有限复杂度的规定集合的度 类型（finitary或infinitary）。 特征化的问题 给定模型的同构副本的度现在似乎 平易近人 奈特和斯拉曼有一个特征， 有限斯科特高度的模型。 人物塑造是 令人不快的复杂，他们希望简化它。 最近的结果使用了哈灵顿的强有力的方法。 此外 为了使用这种方法获得进一步的结果，奈特希望 更好地理解方法本身。 灰 发展了一个相关的方法，并证明了一个定理，给出一般 他的方法是在什么条件下起作用的。 阿什和奈特 开始尝试比较这两种方法。 所有这些 调查进一步揭示了 计算能力，这一问题变得越来越重要， 随着计算能力的实际极限随着 每一代新机器。

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.