U.S.-Czechoslovak Research on Proof Theory and Fragments of Arithmetic

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The primary objective of this U.S.-Czechoslovakia cooperative research project between Dr. Samuel Buss of the University of California at San Diego and Dr. Jiri Becvar of the Czechoslavak Academy of Sciences Institute of Mathematics is to solve some closely related, central problems in mathematical logic involving proof theory and complexity theory. Specifically, joint efforts will address: (1) fragments of Peano arithmetic, (2) fragments of bounded arithmetic and (3) lengths of proofs in propositional and in first-order logic. Recent experience has shown that these topics overlap in content and technique. It is expected that progress in one of the above topics will suggest new directions or results for the others and thereby contribute to our basic knowledge of the metamathematics of number theory. This project in mathematics research fulfills the program objective of advancing scientific knowledge by enabling experts in the United States and Eastern Europe to combine complementary talents and pool research resources in areas of strong mutual interest and competence.