Collaboration in Computability

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The area of computability has blossomed in recent years. Some of the most interesting problems call for combining computability with sophisticated algebra, model theory, descriptive set theory, and/or probability. There is a large group in Novosibirsk working on these problems. There are smaller groups doing related work elsewhere in Russia, in Kazakhstan, and at several universities in the U.S. The grant will be used to help build and maintain working relationships among these researchers. The first goal is to to solve problems. The grant will help us to produce better results, to work more quickly, and to be aware of more important connections.Two earlier NSF grants have, for the past ten years, served to facilitate joint work by researchers from the U.S., Russia, and Kazakhstan. At the time the first proposal was submitted, collaboration among researchers in logic in the U.S. and the former Soviet Union was just beginning, with occasional visits by senior researchers. The first grant had an enormous impact and greatly magnified the ties among researchers in the three countries. The second grant led to much greater involvement of young researchers. The current grant will be used to continue building a network of collaborators who are committed to sharing ideas and working together on fundamental problems. We will continue the emphasis on involving young researchers. We want our graduate students and postdocs to see themselves as part of an international research community.