Robert Lawson Vaught (April 4, 1926 Alhambra, California - April 2, 2002) was a mathematical logician, and one of the founders of model theory. Alhambra is a city located in the western San Gabriel Valley region of Los Angeles County, California. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... In mathematics, model theory is the study of the representation of mathematical concepts in terms of set theory, or the study of the models which underlie mathematical systems. ...

Life

Vaught was a bit of a musical prodigy in his youth, in his case the piano. He began his unversity studies at Pomona College, at age 16. When WWII 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. The Smith Campus Center Fountain at Pomona College during the inauguration of David Oxtoby Pomona College is a small private residential liberal arts college in Claremont, California, located 47 miles (76 km) east of Los Angeles. ... German soldiers at the Battle of Stalingrad World War II was the most extensive and costly armed conflict in the history of the world, involving the great majority of the worlds nations, being fought simultaneously in several major theatres, and costing tens of millions of lives. ... The United States Navy (USN) is the branch of the United States armed forces responsible for naval operations. ... The University of California (UC) is a public university system in the state of California. ... The V-12 Navy College Training Program was designed to supplement the force of commissioned officers in the United States Navy during World War II. Between July 1, 1943 and June 30, 1946, over 125,000 men were enrolled in the V-12 program in 131 colleges and universities in...

In 1946, he began a Ph.D. in mathematics at Berkeley. He initially worked under the topologist John L. Kelley, wring 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. C*-algebras are an important area of research in functional analysis, a branch of mathematics. ... Loyalty oaths is an oath of loyalty to the organization, institution, or state to which an individual is a member. ... Tulane University is a private, nonsectarian, coeducational research university located in New Orleans, Louisiana. ... Alfred Tarski (January 14, 1901, Warsaw Poland – October 26, 1983, Berkeley California) was a logician and mathematician of considerable philosophical importance. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... The University of Washington, founded in 1861, is a major public research university in Seattle, Washington. ...

In 1957, Vaught married Marilyn Maca; they had two children.

Work

To Vaught we owe many of 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 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 states that a complete first order theory cannot have exactly 2 nonisomorphic countable models. In mathematics, model theory is the study of the representation of mathematical concepts in terms of set theory, or the study of the models which underlie mathematical systems. ... In model theory, given two structures and in the same language , we say that is an elementary substructure of (notated sometimes ) if 1. ... In mathematics, the cardinality of a set is a measure of the number of elements of the set. There are two approaches to cardinality – one which compares sets directly using bijections, injections, and surjections, and another which uses cardinal numbers. ...

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.

Reference

• Feferman, Anita Burdman, and Solomon Feferman, 2004. Alfred Tarski: Life and Logic. Cambridge Univ. Press. 24 index entries for Vaught, especially pp. 185-88.

For other uses of the word Solomon, see Solomon (Disambiguation) Solomon Feferman is a mathematician and philosopher at Stanford University. ...

External links

• Robert Lawson Vaught at the Mathematics Genealogy Project
• Obituary