Robert Lawson Vaught (April 4, 1926 – April 2, 2002) was a

mathematical logic Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...

ian and one of the founders of

model theory In mathematical logic, model theory is the study of the relationship between theory (mathematical logic), formal theories (a collection of Sentence (mathematical logic), sentences in a formal language expressing statements about a Structure (mat ...

.In Memoriam: Robert Lawson Vaught, U. C. Berkeley

Life

Vaught was a musical prodigy in his youth, in his case playing the piano. He began his university studies at

Pomona College Pomona College ( ) is a private university, private Liberal arts colleges in the United States, liberal arts college in Claremont, California. It was established in 1887 by a group of Congregationalism in the United States, Congregationalists ...

, at age 16. When

World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...

broke out, he enlisted into the

US Navy The United States Navy (USN) is the naval warfare, maritime military branch, service branch of the United States Department of Defense. It is the world's most powerful navy with the largest Displacement (ship), displacement, at 4.5 millio ...

, which assigned him to the

University of California The University of California (UC) is a public university, public Land-grant university, land-grant research university, research university system in the U.S. state of California. Headquartered in Oakland, California, Oakland, the system is co ...

'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 supervision of 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 Loyalty is a Fixation (psychology), devotion to a country, philosophy, group, or person. Philosophers disagree on what can be an object of loyalty, as some argue that loyalty is strictly interpersonal and only another human being can be the obj ...

. Kelley declined and moved his career to

Tulane University The Tulane University of Louisiana (commonly referred to as Tulane University) is a private research university in New Orleans, Louisiana, United States. Founded as the Medical College of Louisiana in 1834 by a cohort of medical doctors, it b ...

for three years. Vaught then began afresh under the supervision of

Alfred Tarski Alfred Tarski (; ; born Alfred Teitelbaum;School of Mathematics and Statistics, University of St Andrews ''School of Mathematics and Statistics, University of St Andrews''. January 14, 1901 – October 26, 1983) was a Polish-American logician ...

, completing in 1954 a thesis on

, titled ''Topics in the Theory of Arithmetical Classes and Boolean Algebras''. After spending four years at the

University of Washington The University of Washington (UW and informally U-Dub or U Dub) is a public research university in Seattle, Washington, United States. Founded in 1861, the University of Washington is one of the oldest universities on the West Coast of the Uni ...

, 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

. In 1957, he and Tarski introduced

elementary submodel In model theory, a branch of mathematical logic, two structures ''M'' and ''N'' of the same signature ''σ'' are called elementarily equivalent if they satisfy the same first-order ''σ''-sentences. If ''N'' is a substructure of ''M'', one oft ...

s and the

Tarski–Vaught test In model theory, a branch of mathematical logic, two structures ''M'' and ''N'' of the same signature ''σ'' are called elementarily equivalent if they satisfy the same first-order ''σ''-sentences. If ''N'' is a substructure of ''M'', one oft ...

characterizing them. In 1962, he and

Michael D. Morley Michael Darwin Morley (September 29, 1930 – October 11, 2020) was an American mathematician. At his death in 2020, Morley was professor emeritus at Cornell University. His research was in mathematical logic and model theory, and he is best know ...

pioneered the concept of a saturated structure. His investigations on countable models of first-order theories led him to the

Vaught conjecture The Vaught conjecture is a conjecture in the mathematical field of model theory originally proposed by Robert Lawson Vaught in 1961. It states that the number of countable models of a first-order complete theory in a countable language is finit ...

stating that the

number A number is a mathematical object used to count, measure, and label. The most basic examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can ...

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 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", introducing the Vaught transform. He is known for the Tarski–Vaught test for elementary substructures, the

Feferman–Vaught theorem The Feferman–Vaught theorem in model theory is a theorem by Solomon Feferman and Robert Lawson Vaught that shows how to reduce, in an algorithmic way, the first-order theory of a product of structures to the first-order theory of elements of t ...

, the Łoś–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).

Notes

References

* Feferman, Anita Burdman, and

Solomon Feferman Solomon Feferman (December 13, 1928July 26, 2016) was an American philosopher and mathematician who worked in mathematical logic. In addition to his prolific technical work in proof theory, computability theory, and set theory, he was known for h ...

, 2004. ''Alfred Tarski: Life and Logic''. Cambridge Univ. Press. 24 index entries for Vaught, especially pp. 185–88.

External links

* * {{DEFAULTSORT:Vaught, Robert Lawson 1926 births 2002 deaths 20th-century American mathematicians 21st-century American mathematicians Model theorists People from Alhambra, California Pomona College alumni

Life

Work

See also

Notes

References

External links