Mathematics Professor Publishes Book

Stephen Simpson, professor of mathematics, has authored a book, Subsystems of Second Order Arithmetic, published by Springer-Verlag of Heidelberg, Germany.

Part of the publisher's "Perspectives in Mathematical Logic" series, Simpson's book represents an original contribution to foundations of mathematics, with emphasis on the role of set-existence axioms. Part A demonstrates that many familiar theorems of algebra, analysis, combinatorics, and functional analysis are logically equivalent to the axioms needed to prove them because of a phenomenon known as "reverse mathematics." Part B provides a thorough study of models of those and other systems, and the book includes an extensive bibliography and a detailed index.

"From the point of view of the foundations of mathematics, this definitive work by Simpson is the most anxiously awaited monograph for over a decade," said Harvey Friedman, professor of mathematics at Ohio State University. "The book is both suitable for the beginning graduate student in mathematical logic, and encyclopedic for the expert."

An authority on subsystems of second-order arithmetics and their role in the foundations of mathematics, Simpson has published extensively regarding mathematical logic and the foundations of mathematics. He joined the Penn State faculty as an assistant professor in 1975 and was promoted to associate professor in 1977 and to professor in 1980. Prior to that, he served as an instructor and lecturer at Yale University from 1971 to 1972, the University of California at Berkeley from 1972 to 1974, and the University of Oxford in England from 1974 to 1975. He earned his doctoral degree in mathematics at the Massachusetts Institute of Technology in 1971. He earned both his master's and bachelor's degrees in mathematics at Lehigh University.

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