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

美国的主要目标是-捷克斯洛伐克合作社 一项研究项目， 加州圣地亚哥和捷克斯拉夫人的吉里·贝伐尔博士 科学院数学研究所是解决一些 数学逻辑中密切相关的中心问题， 证明理论和复杂性理论。 具体而言，共同努力 将解决：（1）皮亚诺算术的片段，（2）片段， 有界算术和（3）长度的证明命题和 在一阶逻辑中。 最近的经验表明， 主题在内容和技术上重叠。 预计在 上述任何一个主题的进展将提出新的方向， 为他人提供结果，从而有助于我们的基本知识 数论的元数学 这个数学研究项目实现了计划目标 促进科学知识的发展， 国家和东欧联合收割机互补人才和汇集 在共同感兴趣和能力强的领域的研究资源。

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.