The creation of a new Logic and Foundations Option within the current mathematics graduate program is aimed towards creating an environment where research and education in mathematical logic and foundations of mathematics can prosper and thrive beyond the current level.
The design of the new option takes into account the success of the current graduate program in providing an excellent doctoral education. However it also acknowledges its limitations in supporting some areas of graduate education in mathematical logic and foundations of mathematics. Within such a context, the establishment of the new Logic and Foundations Option is intended to augment and enrich the current graduate program rather than alter it.
This new option will have a major impact in research and education in various branches of mathematical logic, including recursive function theory, set theory, proof theory, and model theory. Since a major goal of such research is to obtain insight into the foundations of mathematics, such kinds of research are very unlikely to be pursued in other Science and Engineering Departments.
It is relevant to point out that Penn State Mathematics Department has a long history of research and graduate education in mathematical logic and foundations of mathematics, going back to key figures such as Haskell Curry. For many years, Penn State was considered one of the best places in the world to study these subjects.
For the Logic and Foundations Option to succeed, it is essential to ensure a stable supply of graduate students. Because of realistic constraints in personal resources and time, the present qualifying exam system has negatively impacted recruitment of candidates. Discussion with department faculty in all areas reveals that a reasonable solution to accommodate the Logic and Foundations Option can be found without jeopardizing the present one, while simultaneously ensuring and strengthening the quality level of the current system.
Typical candidates for the Logic and Foundations Option would be students with a strong undergraduate mathematics background who are interested in mathematical logic and foundations of mathematics.