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.
