Mathematical Sciences: Recursive Model Theory

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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. ***