Mathematical Sciences: Recursive Model Theory

Knight的研究项目，包括她自己和她的学生和合作者的研究项目，涉及递归模型理论的一系列主题。在这个项目中，她将在几个抽象层次上工作，从寻找新的元定理来澄清理论和模型之间的联系，到解决特定理论的模型问题。其中一部分涉及找到一种算法来构造一个初始描述无效的数学对象（例如，在约简阿贝尔p群的设置中）。另一部分涉及到在递归理论复杂性和模型理论可定义性之间建立精确的联系。目前的拨款为奈特的研究小组提供了一些必要的旅行和供应需求。他们的研究活动涉及逻辑的一个领域，其主要焦点是可计算性，并与建立数学理论模型的方法有关。＊＊＊

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. ***