Mathematical Sciences: Recursive Model Theory

小行星9504594 奈特的研究计划，无论是在她的手中，在她的学生和合作者，涉及一系列的主题递归模型理论。在这个项目中，她将致力于几个层次的抽象，从寻求新的元定理，以澄清理论和模型之间的联系，以解决有关特定理论的模型问题。 一部分涉及找到用于构造数学对象的算法（例如，在约化阿贝尔p-群的设置中），其初始描述是无效的。 另一部分涉及精确递归理论的复杂性和模型理论的可定义性之间的联系。 目前的赠款为奈特的研究小组提供了一些基本的旅行和用品需求。 他们的研究活动涉及逻辑领域，其主要重点是可计算性，并与数学理论的建模方法有关。 ***

9504594 Knight Knight's research program, both in her hands and in those of her students and collaborators, involves a range of topics in recursive model theory. In this project, she will be working on several levels of abstraction, from seeking new metatheorems to clarify connections between theories and their models, to addressing problems about models of specific theories. One part involves finding an algorithm for constructing a mathematical object (e.g., in the setting of reduced Abelian p-groups) whose initial description is not effective. Another part concerns making precise the connections between recursion-theoretical complexity and model-theoretical definability. The current grant provides some essential travel and supply needs for Knight's research group. Their research activities concern an area of logic whose main focus is computability, and which has ties to methods of building models for mathematical theories. ***