Our department has a long tradition of excellence in mathematical logic going back to Haskell Curry, one of the first Evan Pugh professors, who was also one of the leading American logicians through the 40's, 50's and 60's. Dick Mansfield arrived here in the early 70's, and Tom Jech and I were hired in 1975. Many students came to Penn State specifically in order to study logic. Many outstanding logicians were trained at Penn State. I myself have supervised 12 PhD students, most of whom continue to teach and perform research in this field; see the appendix below. Tom Jech has also had a distinguished record of accomplishment in supervising PhD students; see the appendix below. Dick Mansfield has also supervised several PhD students.
During the period 1975-1990, logic students had the possibility of taking a logic qualifying exam based on what was then known as the first-year graduate logic sequence, Math 557-558. This sequence was very successful in focusing their studies and teaching them basic concepts and methods of mathematical logic. At the same these students took other courses and qualifying exams, principally algebra and analysis. They then went on to advanced courses and seminars in other branches of mathematics as well as logic and set theory. This system produced many excellent logic PhDs.
In 1990, the present system of qualifying exams in algebra, analysis and topology was introduced. As part of this reform, the logic qualifying exam was abolished, and the 557-558 sequence was decoupled into two independent elective courses. Since 1990, few if any students have taken these courses in sequence. Because of the new situation created in 1990, it has been extraordinarily difficult to develop new PhD students in this area. The biggest problem is that potential logic students must spend most of their first two years preparing for qualifying exams in algebra, analysis, and topology. This preparation is time-consuming, and much of the material in those exams is irrelevant to their future specialty. During those two years, the logic students must put logic on hold for the most part. The effect is to severely impede their studies and postpone the time when they can begin thesis research. The only way around this problem is for a student to arrive at Penn State having already mastered a substantial amount of the graduate-level material that is covered in the qualifying exams. All recent PhDs in logic were people who either entered under the pre-1990 system, or who entered at a postgraduate level in terms of previous training and background.