# Program in Logic and Foundations of Mathematics

The Departments of Philosophy and of Mathematics together offer a joint Ph.D. degree in Logic and the Foundations of Mathematics. Students in this program submit a single dissertation prepared under the supervision of members of both departments. Students enrolled in the Philosophy PhD program at Notre Dame can apply to the joint-degree program (typically during their third year of study). The joint-degree program does not accept applications from students outside of Notre Dame or admit students to the University.

The joint Ph.D. program continues a long tradition of the advanced study of formal logic at the University of Notre Dame.

#### Faculty

Tim Bays (Philosophy)

Jc Beall (Philosophy)

Patricia Blanchette (Philosophy)

Peter Cholak (Mathematics)

Natasha Dobrinen (Mathematics)

Curtis Franks (Philosophy)

Joel David Hamkins (Philosophy and Mathematics)

Julia Knight (Mathematics)

Anand Pillay (Mathematics and Philosophy)

Nicholas Ramsey (Mathematics)

Sergei Starchenko (Mathematics)

#### Admission

Philosophy students interested in the joint program begin preparing to apply immediately upon beginning their studies at Notre Dame. In addition to philosophy coursework, they take at least the two semester logic sequence, and sometimes other courses, in the Mathematics Department in their first year. They also take part in the Mathematics Department's research seminars. By the second year, they have taken several courses in the Mathematics Department and become integrated into the research group of a Mathematics faculty member whom they intend to be their mathematics supervisor.

Most students will then choose to apply to the Master of Science in Interdisciplinary Mathematics (MSIM). This application describes a list of courses and a research project that the student and his or her mathematics supervisor propose. While working towards the MSIM, the student decides either to complete the degree as initially described or to expand the project into a joint program dissertation. In the latter case, the student applies to the joint-degree program.

#### Requirements

Students in the joint program are required to take only 27 credits in Philosophy. Joint Program students need to take only two of the three seminars in the history of philosophy that are required for the regular Philosophy PhD. program, and the 3 credit seminar "Intermediate Logic" is not required. Students are required to take the two course logic sequence, the two course algebra sequence, and 9 additional credits in the Mathematics Department.

Joint program students take the Mathematics Department's oral candidacy exam instead of the Philosophy Department's oral exam. This consists of both the basic and advanced exams in logic and the basic exam in one other area.

#### Alumni

Matteo Bianchetti, MSIM: "Infinite Time Computation: Strong and Weak Infinite Time Turing Machines" (C. Franks, J. Knight); Ph.D. in Philosophy: "Geometric representations in mathematical problem-solving. Intuition and creativity" (C. Franks), Current Placement: non-academic

Paul Trần-Hoàng, MSIM: "Model-Theoretic Galois Cohomology" (A. Pillay, C. Franks); Ph.D. in Philosophy: "Model-Theoretic Approaches to Theoretical Equivalence and Reduction" (T. Bays, C. Franks). Current placement: Permanent Faculty, Department of Philosophy, Lone Star College

Graham Leach-Krouse, Joint Ph.D.: "Conceptions of Absolute Provability" (T. Bays, M. Detlefsen, P. Larson). Current placement: Associate Professor, Department of Philosophy, Kansas State University.

Chris Porter, Joint Ph.D.: "Mathematical and Philosophical Perspectives on Algorithmic Randomness" (P. Cholak, M. Detlefsen, C. Franks). Current placement: Assistant Professor, Department of Mathematics and Computer Science, Drake University.

Sean Walsh, Joint Ph.D.:** **"Arithmetical Knowledge and Arithmetical Definability: Four Studies" (P. Cholak, M. Detlefsen). Current placement: Associate Professor, Logic and Philosophy of Science, UCLA

Andy Arana, Joint PhD: "Arithmetical Investigations: A Study of Models of Arithmetic and Purity of Methods" (M. Detlefsen, J. Knight). Current placement: Professor of Philosophy, University of Lorraine and Archives Henri-Poincaré.