# Robert Lawson Vaught

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**Robert Lawson Vaught** (April 4, 1926 – April 2, 2002) was an American [mathematical logician](/source/Mathematical_logic) and one of the founders of [model theory](/source/Model_theory).[1]

## Life

Vaught was a musical prodigy in his youth, in his case playing the piano. He began his university studies at [Pomona College](/source/Pomona_College), at age 16. When [World War II](/source/World_War_II) broke out, he enlisted into the [US Navy](/source/US_Navy), which assigned him to the [University of California](/source/University_of_California)'s [V-12](/source/V-12_Navy_College_Training_Program) 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 supervision of the topologist [John L. Kelley](/source/John_L._Kelley), writing on [C* algebras](/source/C*_algebra). In 1950, in response to [McCarthyite](/source/McCarthyism) pressures, Berkeley required all staff to sign a [loyalty oath](/source/Loyalty_oath). Kelley declined and moved his career to [Tulane University](/source/Tulane_University) for three years. Vaught then began afresh under the supervision of [Alfred Tarski](/source/Alfred_Tarski), completing in 1954 a thesis on [mathematical logic](/source/Mathematical_logic), titled *Topics in the Theory of Arithmetical Classes and Boolean Algebras*. After spending four years at the [University of Washington](/source/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.

## Work

Vaught's work is primarily focused on [model theory](/source/Model_theory). In 1957, he and Tarski introduced [elementary submodels](/source/Elementary_submodel) and the [Tarski–Vaught test](/source/Tarski%E2%80%93Vaught_test) characterizing them. In 1962, he and [Michael D. Morley](/source/Michael_D._Morley) pioneered the concept of a [saturated structure](/source/Saturated_structure). His investigations on countable models of first-order theories led him to the [Vaught conjecture](/source/Vaught_conjecture) stating that the [number](/source/Cardinality) 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. Vaught's ["Never 2" theorem](/source/Vaught's_theorem) states that a complete first-order theory cannot have exactly two nonisomorphic countable models.

He considered his best work his paper "Invariant sets in topology and logic"[citation needed], introducing the [Vaught transform](/source/Vaught_transform). He is known for the Tarski–Vaught test for elementary substructures, the [Feferman–Vaught theorem](/source/Feferman%E2%80%93Vaught_theorem), the [Łoś–Vaught test](/source/%C5%81o%C5%9B%E2%80%93Vaught_test) for completeness and decidability, the Vaught two-cardinal theorem, and his conjecture on the nonfinite axiomatizability of totally [categorical theories](/source/Categorical_theory) (this work eventually led to [geometric stability theory](/source/Geometric_stability_theory)).

## See also

- [Łoś–Vaught test](/source/%C5%81o%C5%9B%E2%80%93Vaught_test)

## Notes

1. [In Memoriam: Robert Lawson Vaught, U. C. Berkeley](http://senate.universityofcalifornia.edu/inmemoriam/robertlawsonvaught.html) [Archived](https://web.archive.org/web/20140714201845/http://senate.universityofcalifornia.edu/inmemoriam/robertlawsonvaught.html) 2014-07-14 at the Wayback Machine

## References

- [Feferman, Anita Burdman](/source/Anita_Burdman_Feferman), and [Solomon Feferman](/source/Solomon_Feferman), 2004. *Alfred Tarski: Life and Logic*. Cambridge Univ. Press. 24 index entries for Vaught, especially pp. 185–88.

## External links

- Addison, J. W. (Fall 2002). ["In Memoriam: Robert Lawson Vaught"](https://math.berkeley.edu/sites/default/files/pages/Fall02.pdf). *Berkeley Mathematics Newsletter*. p. 13.

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