Mathematical Sciences: Recursion Theory
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8900349                                                                         Lerman                                                                               Research in Classical Recursion Theory will be pursued.                    The main goals of this work are to analyze further the types of                 search procedures needed to obtain results in Recursion Theory,                 and to see how well the information content of a set is                         mirrored by the degree of that set.  The first goal is to                       develop a O(n) -priority argument for all n: Lerman will try to                 do so in the context of deciding the existential theory of the                  recursively enumerable degrees with Steffen Lempp.  He will                     then try, with Lempp and Kucera, to find a priority-free proof                  of this theory.                                                                      The second goal will be pursued by studying automorphisms                  of sets of degrees, primarily the recursively enumerable                        degrees.  This project is already underway, jointly with Lempp,                 Shore and Soare, and the hope is to produce a nontrivial                        automorphism.
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