U.S.-Finland Cooperative Research in Finite Model Theory (Computer Science)

该奖项支持加州大学圣克鲁斯分校的Phokion Kolaitis教授与芬兰赫尔辛基大学数学系Jouko Vaananen教授在应用数学方面的合作。他们建议从抽象模型理论的角度对有限模型理论进行系统的研究。他们在这些领域的互补专业知识的结合应该会对有限模型理论产生重大的概念和理论贡献。有限模型理论是研究一阶逻辑及其在有限结构上的扩展的理论。它是计算机科学中逻辑中的一个研究领域，与数理逻辑、数据库理论和计算复杂性有许多交互作用。逻辑学家已经发展了这样一种关于任意结构的扩展逻辑的理论，称为抽象模型理论。到目前为止，还没有关于有限结构上的扩展逻辑的一般理论。拟议的合作研究将扩展这一重要逻辑领域的现有框架。

This award supports Professor Phokion Kolaitis, University of California, Santa Cruz, to collaborate in applied mathematics with Professor Jouko Vaananen, Department of Mathematics, University of Helsinki, Finland. They propose to undertake a systematic investigation of finite model theory from the perspective of abstract model theory. The combination of their complementary expertise in these areas should produce significant conceptual and theoretical contributions to finite model theory.. Finite model theory is the study of first-order logic and its extensions on finite structures. It is an area of research within logic in computer science that has had numerous interactions with mathematical logic, database theory, and computational complexity. Logicians have developed such a theory of extended logics on arbitrary structures, known as abstract model theory. So far no general theory of extended logics on finite structures exists. The proposed collaborative research will expand the current framework of this important area of logic.