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

加州大学圣地亚哥分校的Samuel Buss博士和捷克科学院数学研究所的Jiri Becvar博士开展的这项美国-捷克斯洛伐克合作研究项目的主要目标是解决涉及证明论和复杂性理论的数理逻辑中一些密切相关的核心问题。具体地说，联合努力将解决：(1)Peano算术的片段，(2)有界算术的片段，以及(3)命题和一阶逻辑中的证明长度。最近的经验表明，这些主题在内容和技术上是重叠的。期望在上述主题中的一个方面的进展将为其他主题提供新的方向或结果，从而有助于我们对数论的元数学的基本知识。这个数学研究项目通过使美国和东欧的专家能够将互补的人才结合在一起，并在相互感兴趣和能力很强的领域汇集研究资源，实现了促进科学知识的计划目标。

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.