Cuny Collaboration in Mathematical Logic Arthur W. Apter, Baruch College Joel D. Hamkins, College of Staten Island Roman Kossak, Bronx Community College George Leibman, Bronx Community College

We propose to undertake a broad new collaboration in our common speciality, mathematical logic, a collaboration we hope will further enhance research in logic at CUNY. Our university is one of the few in the world which houses active researchers in so many different branches of mathematical logic, and our group alone represents already three major subfields: set theory, model theory and computability theory. This project is intended to profit from this unique situation and further strengthen the ties through interdisciplinary research projects as well as joint research in each of these subfields. There is a long-standing tradition of top quality research in logic at CUNY, stretching back many decades. In the past decade, the addition of new faculty has invigorated the program, and our recent collaborations have become more intense, supported in part by previous Collaborative Incentive grants. As faculty members of the CUNY Graduate Center, Hamkins and Kossak have been very active in the development of the graduate logic program in mathematics, which as a result, has grown substantially in the last years. Schoutens and Miller, who have just become members of the graduate faculty in respectively the Mathematics Department and the Computer Science Department, will contribute further to this positive trend. The members of this group have also been very active in various seminars at the Graduate Center. Hamkins, Kossak and Schoutens are the co-founding directors of the CUNY Logic Workshop, which since its inception a decade ago has been acquiring an ever growing audience (with participation from faculty and students not only from CUNY, but from universities throughout the New York metropolitan region, including Columbia, Rutgers and NYU), bringing many distinguished visitors to CUNY. Hamkins is also operating a set theory seminar with his graduate students. Kossak and Schoutens have revived a model theory seminar (three years ago they had already started such a seminar, but they had to put this initiative on hold when Schoutens accepted a two year visiting position at OSU), in which Miller and several graduate students participate, with the aim of studying in depth new developments in model theory. Apter, Hamkins and Kossak are jointly members of the advisory board of the Mid-Atlantic Mathematical Logic Seminar (MAMLS), an NSF-funded traveling conference which meets up to four times yearly (Apter is