Carnegie Mellon University

Ph.D. Program in Pure and Applied Logic

The Ph.D. Program in Pure and Applied Logic is an interdisciplinary program designed to support students seeking a career in Mathematics, but interested in working in an area of logic supported by the Department of Philosophy. As part of the program, students earn an M.S. degree from the Department of Mathematical Sciences.

Research areas include:

  • automated deduction and automated reasoning
  • category theory and categorical logic
  • computability and computable analysis
  • constructive logic and type theories
  • homotopy type theory
  • proof theory


The program's flexible requirements provide a broad curricular grounding, steady involvement in research, and the opportunity to practice the craft of teaching in an excellent undergraduate environment. Students are expected to complete a thesis by the middle of their third year, and a PhD thesis by the end of their fifth year.


There are complementary degree programs in Pure and Applied Logic in the Departments of Mathematical Sciences and Computer Science. Research specializations in those departments include set theory, descriptive set theory, model theory, recursion theory, combinatory logic and lambda calculus, formal verification, automated reasoning, type theory, semantics of programming languages, and many other logic-related topics.