SM: Logic Year at the University of Florida

University Of Florida, Gainesville FL

Investigators

Abstract

Special Year in Mathematical Logic, University of Florida, 2006-2007 The special year in mathematical logic will be devoted to the exploration of various channels of communication between several fields of logic as well as the rest of the mathematical sciences. Mathematical logic is entering a phase of increasingly intense conversation with other parts of mathematics. In one workshop, we will concentrate on the relationship between computability, effective descriptive set theory and computable analysis on one hand and numerical methods and analysis on the other, such as the study of effectively closed sets and effectivity of reals and real functions. Potential special topics will include algorithmic randomness, quantum computation, reverse mathematics. The second workshop will relate the current trends in definable forcing and determinacy with measure theory, potential theory and dynamical systems, as well as with the games used in biomathematics or economics. Special topics include Borel equivalence relations and definable forcing. The third workshop will further explore the connections between singular cardinals and inner models. Recent work on large cardinals and inner models has helped to advance the frontier of set theory and its applications to mathematics. The special year will bring together leading scientists from many areas of mathematical logic, in an effort to advance our understanding of this fundamental discipline. Just as mathematics is the language of science and provides the foundation of science, so logic is the language of mathematics and provides the foundation of mathematics. The subject of logic has its roots in classical philosophy and today has branches in many disciplines, including mathematics and philosophy, as well as computer science, linguistics, and law. Logic is used in expert systems which, for example, help doctors diagnose illness with the aid of computers. Current research on hybrid algorithms is using logic in the development of software which will map out the flight plan of an airplane in real time. While the program is based in the mathematics department, other departments, including philosophy and computer science, will also participate. The broader impact of the project includes an emphasis on participation of graduate students, junior researchers and women mathematicians. There will also be a focus on participants from the Southeast region. We will publish proceedings of the work presented during the special year.