The Work of Harvey Friedman

Abstract

Publisher Summary This chapter focuses on the work of mathematical logician Harvey Friedman, who was recently awarded the National Science Foundation's annual Waterman Prize, honoring the most outstanding American scientist under thirty-five years of age in all fields of science and engineering. Friedman's contributions span all branches of mathematical logic (recursion theory, proof theory, model theory, set theory, and theory of computation). He is a generalist in an age of specialization, yet his theorems often require extraordinary technical virtuosity, of which only a few selected highlights are discussed. Friedman's ideas have yielded radically new kinds of independence results. The kinds of statements that were proved to be independent before Friedman were mostly disguised properties of formal systems (such as Godel's theorem on unprovability of consistency) or assertions about abstract sets (such as the continuum hypothesis or Souslin's hypothesis). In contrast, Friedman's independence results are about questions of a more concrete nature involving, for example, Borel functions or the Hilbert cube.