Robert Lawson Vaught
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Robert Lawson Vaught (April 4, 1926, Alhambra, California – April 2, 2002) was a mathematical logician, and one of the founders of model theory.
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[edit] 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. When World War II broke out, he enlisted US Navy which assigned him to the University of California's V-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 on C* algebras. In 1950, in response to McCarthyite pressures, Berkeley required all staff to sign a loyalty oath. Kelley declined and moved his career to Tulane University for three years. Vaught then began afresh under Alfred Tarski, completing in 1954 a thesis on mathematical logic, titled Topics in the Theory of Arithmetical Classes and Boolean Algebras. After a four years at the University 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.
[edit] Work
To Vaught we owe many of the fundamental concepts and results in model theory. In 1957, he and Tarski introduced elementary submodels and the Tarski-Vaught test characterizing them. In 1962, he and Morley pioneered the concept of a saturated 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.[1]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, the Feferman-Vaught product theorem, the Los-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 to geometric 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.
[edit] 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.
[edit] Notes
- ^ See preprint available at http://www.maths.ox.ac.uk.
