- Robert Lawson Vaught
Robert Lawson Vaught (
April 4 1926 ,Alhambra, California –April 2 2002 ) was amathematical logic ian, and one of the founders ofmodel theory .Life
Vaught was a bit of a musical prodigy in his youth, in his case the piano. He began his university studies at
Pomona College , at age 16. WhenWorld War II broke out, he enlistedUS Navy which assigned him to theUniversity of California 'sV-12 program. He graduated in 1945 with an AB in physics.In 1946, he began a Ph.D. in mathematics at Berkeley. He initially worked under the topologist
John L. Kelley , writing onC* algebra s. In 1950, in response to McCarthyite pressures, Berkeley required all staff to sign aloyalty oath . Kelley declined and moved his career toTulane University for three years. Vaught then began afresh underAlfred Tarski , completing in 1954 a thesis onmathematical logic , titled "Topics in the Theory of Arithmetical Classes and Boolean Algebras". After a four years at theUniversity of Washington , Vaught returned to Berkeley in 1958, where he remained until his 1991 retirement.In 1957, Vaught married Marilyn Maca; they had two children.
Work
Vaught's work is primarily focused around the field of
model theory . In 1957, he and Tarski introducedelementary submodel s and theTarski-Vaught test characterizing them. In 1962, he and Morley pioneered the concept of asaturated structure . His investigation of countable models of first order theories led him to conjecture that the number of countable models of a complete first order theory (in a countable language) is always either finite, or countably infinite, or equinumerous with the real numbers. It is thought a counter-example to the Vaught conjecture has now been found. [ See preprint available at [http://www.maths.ox.ac.uk/~knight/stuff/example.ps http://www.maths.ox.ac.uk] .] Vaught's "Never 2" theorem states that a complete first order theory cannot have exactly 2 nonisomorphic countable models.He thought his best work was his paper "Invariant sets in topology and logic", introducing the
Vaught transform . He will be remembered for the Tarski-Vaught criterion for elementary extensionality, theFeferman-Vaught product theorem , theLos-Vaught test for completeness and decidability, the Vaught two-cardinal theorem, and his conjecture on the nonfinite axiomatizability of totally categorical theories (this work eventually led togeometric stability theory ).Vaught was a capable teacher of undergraduates, and his writing was reputed for elegance and clarity. His "Set Theory: An Introduction" (2001, 2nd ed.) attests to his abilities in this regard.
References
*Feferman, Anita Burdman, and
Solomon Feferman , 2004. "Alfred Tarski: Life and Logic". Cambridge Univ. Press. 24 index entries for Vaught, especially pp. 185-88.Notes
External links
*MathGenealogy|id=19857
* [http://math.berkeley.edu/publications/newsletter/2002/memoriam.html Obituary]
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