Harvey Friedman

Harvey Martin Friedman ( born September 23, 1948) is an American mathematician and philosopher who is concerned with mathematical logic and the foundations of mathematics.

Life and work

Friedman received his PhD in 1967 in mathematics at Gerald E. Sacks at the Massachusetts Institute of Technology ( subsystem of Analysis ). After that, he was Assistant Professor ( which gives him a place in the Guinness Book of World Records as the youngest professor earned ) and from 1969 Associate Professor of Philosophy at Stanford University. In 1970 he was associate professor of mathematics at the University of Wisconsin -Madison and from 1973 professor at the State University of New York at Buffalo.

Since 1977 he has been Professor of Mathematics at Ohio State University. From 1985 he was a professor of philosophy and computer science, and since 1991 also professor of music. In 1987 he was appointed Distinguished Professor.

He has been a visiting scientist and consultant at IBM and at Bell Laboratories. He has been a visiting professor at the University of Pennsylvania, the University of Minnesota and Princeton University.

Friedman worked on axiomatic set theory, model theory ( where he founded the Borel Model Theory ), proof theory, intuitionism, computer science and computability theory. He is known as a representative of substantiated by the reverse mathematics, the axioms required to prove excludes the deemed necessary theorems ( for example, axioms of large cardinals ). His work led back in the early 1970s to completely new independence sets much more concrete nature, as for example in the classic work of Kurt Godel and Paul Cohen, first in theory, Borel - measurable functions, then also in the discrete mathematics (sets, which could be proved by ZFC alone is not, but as with axioms large Cardinal ). Around 2000 he summarized his studies on these subjects together in its Boolean Relation Theory.

In the 1980s, he showed that a variant of the set of Joseph Kruskal about the arrangement of sets of trees is undecidable in Peano arithmetic.

He showed that Borel determinacy can not be proven in systems with only countably many iterations of the power set formation.

In 1984 he received the Alan T. Waterman Award of the National Science Foundation. 1986/87 he was a Guggenheim Fellow. In 2002 he was Lecturer Godel and 2007 he held the Tarski Lectures at the University of California, Berkeley. In 1974 he was invited speaker at the International Congress of Mathematicians in Vancouver ( Some systems of second order arithmetic and Their use).

He is the brother of the mathematician Sy Friedman.