Robert Lawson Vaught
Robert Lawson Vaught ( born April 4, 1926 in Alhambra, California, † April 2, 2002 in Berkeley ) was an American mathematical logician.
Life and work
Vaught studied in World War II in a program of the U.S. Navy at the University of California, Berkeley, Physics ( completion 1945), continued at Cornell University. After his service in the Navy, he studied mathematics at Berkeley in 1946. First, he wanted to do a doctorate at John L. Kelley on operator algebras, as this was but expelled from the university because he the oath of loyalty did not pay during the McCarthy era, Vaught earned his doctorate under Alfred Tarski in 1954 in mathematical logic ( Topics in the theory of arithmetical classes and boolean algebras ). After four years at the University of Washington, most recently as Assistant Professor, he was in 1958 again in Tarski's group at Berkeley, where he became professor in 1963 and remained until his retirement in 1991.
Vaught was since his work with Tarski one of the pioneers of the model theory. He established here many important concepts ( so saturated structures in 1962 with Michael Morley ) and is also known for a conjecture of 1961 that Vaught 's conjecture ( that the number of countable models of complete theories, first-order either finite, countably infinite, or of the cardinality of the real numbers ). He proved in his Never Theorem 2 that a complete first order theory can not have exactly two non- isomorphic countable models. Furthermore, the criterion of Vaught, a completeness criterion for theories of first-order predicate logic, associated with his name.
1956/57, he was a Fulbright Scholar in Amsterdam and in 1967 as the Guggenheim Fellow in Zurich. In 1978 he received the Karp Prize for his work on the logic of infinite long expressions with the help of a he introduced topological structure ( Vaught transformation). In 1966 he was invited speaker at the International Congress of Mathematicians in Moscow ( model theory and set theory ).
His doctoral Jack Silver, James Baumgartner and Michael Morley counts (formally by Saunders MacLane, but Vaught supervised the work ).
Writings
- Set Theory - an introduction, 2nd edition, Birkhäuser 1994, 2001