Harvey Friedman (mathematician)

from Wikipedia, the free encyclopedia
Harvey Friedman (mathematician)

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

Live and act

Friedman received his PhD in mathematics in 1967 with Gerald E. Sacks at the Massachusetts Institute of Technology (Subsystems of Analysis). He was then Assistant Professor (for which he received an entry in the Guinness Book of Records as the youngest professor) and from 1969 Associate Professor of Philosophy at Stanford University . In 1970 he became 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 a math professor at Ohio State University . From 1985 he was professor of philosophy and computer science there and from 1991 also professor of music. In 1987 he was made a Distinguished Professor.

Among other things, he was visiting scientist and consultant at IBM and Bell Laboratories . He was visiting professor at the University of Pennsylvania , the University of Minnesota and Princeton University , among others .

Friedman dealt with axiomatic set theory, model theory (where he founded Borelian model theory), proof theory, intuitionism, computer science and computability theory. He is known as a representative of the reverse mathematics he founded , which deduces the axioms required for the proof from the theorems considered necessary (for example also axioms of large cardinal numbers). As early as the early 1970s, his work led to completely new independence theorems of a much more concrete nature than, for example, in the classical works of Kurt Gödel or Paul Cohen , initially in the theory of Borel measurable functions, then also in discrete mathematics (sentences, which could not be proved with ZFC alone, but with axioms of large cardinal numbers). Around 2000 he summarized his investigations in this regard in his Boolean Relation Theory .

In 1981 he showed that a variant of Joseph Kruskal's theorem formulated with finite sets , that in an infinite set of trees there is one that contains another tree of the set, cannot be decidable in Peano arithmetic. The theorem could be proven with ZFC , but Friedman later found undecidable theorems for more general networks than trees. Another Friedman method for generating undecidable sentences uses functions on infinite sets (Boolean Relation Theory).

He showed that Borel determinacy cannot be proven in systems with only countably infinite iterations of power set formation.

In 1984 he received the Alan T. Waterman Award from the National Science Foundation . In 1986/87 he was a Guggenheim Fellow. In 2002 he was a Gödel Lecturer and in 2007 he gave 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 .

literature

Web links

Individual evidence

  1. ^ First at the International Congress of Mathematicians in Vancouver 1974 Some Systems of Second Order Arithmetic and Their Use . Further for example: Friedman, Stephen G. Simpson : Issues and problems in reverse mathematics. In: Cholak, Lempp, Lerman, Shore (Eds.): Computability theory and its applications. AMS 2000, pp. 127-144, or Simpson: Subsystems of second order logic. Cambridge University Press 2009
  2. ↑ Harrington, Nerode Harvey Friedman , Notices AMS, Vol. 31, 1984, p. 563.
  3. ^ Marianne Freiberger, Picking Holes in Mathematics, Plus Magazine
  4. ^ Friedman: Higher set theory and mathematical practice. In: Annals of Mathematical Logic. Volume 2, 1971, p. 326
personal data
SURNAME Friedman, Harvey
ALTERNATIVE NAMES Friedman, Harvey Martin (full name)
BRIEF DESCRIPTION American mathematician and philosopher
DATE OF BIRTH September 23, 1948