Computability, Logic and Complexity

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9602579 Shore This award will support the travel of the principal investigator, Professor Richard Shore, Department of Mathematics, Cornell University, and two junior investigators, Professor Peter Cholak, Department of Mathematics, University of Notre Dame, and Professor Andre Nies, Department of Mathematics, University of Chicago, to New Zealand over a three year-period. In New Zealand, they will work with colleagues in the logic groups at Victoria University, notably Professor Rodney Downey, and at Auckland University, including Dr. Bakhadyr M. Khoussainov who recently took up his position after serving as an Assistant Professor at Cornell University. They will each work on a number of topics in recursion theory united by a common theme of studying how computation interacts with various areas of logic, mathematics and computer science. Most of the work will be done by applying the methods of computability theory such as the priority method and other tools of logic such as the coding theories to the study of effectiveness issues in other mathematics settings. This project combines the strengths of three of the leading U.S. groups in logic with one of the leading centers of logic research in the Pacific Basin at Victoria University in Wellington.