Berkeley - Robert Lawson Vaught, professor emeritus of mathematics at the University of California, Berkeley, died Tuesday (April 2) at Alta Bates Medical Center in Berkeley after an extended illness. He was 75.Vaught was widely regarded as one of the great pioneers in the field of model theory, one of the major branches of mathematical logic and a field that applies ideas of traditional logic to the study of algebraic and other mathematical structures.

Born in Alhambra, Calif., on April 4, 1926, Vaught began his college studies at Pomona College in 1942 before leaving in 1944 for service in World War II. The U.S. Navy assigned him to the V12 program at UC Berkeley, where he completed an AB degree in physics in 1945 before being sent to Midshipmen School at Cornell University in New York. He completed his naval service in 1946 with the rank of Lieutenant jg and returned to UC Berkeley for graduate studies.

After some early successful research at UC Berkeley in mathematical analysis, Vaught came under the influence on campus of the great logician Alfred Tarski, and completed his doctoral dissertation under him, obtaining a PhD in mathematics in 1954. Tarski had recently founded the theory of models and Vaught, as a student and in his later work, accelerated its development by both proving a number of basic principles of the theory and formulating several of its most important and fundamental concepts - principles and concepts which are still in constant use today.

After obtaining his doctorate, Vaught joined the faculty of the University of Washington in Seattle, serving there as an instructor and assistant professor until 1958, when he accepted a call to return to UC Berkeley, where Tarski was building a group which would soon bring the university recognition as the world's leading center for research in mathematical logic. Vaught became a central member of the group, attaining the rank of professor in 1963 and teaching there until his retirement in 1991.

Vaught was a Fulbright Research Scholar at the University of Amsterdam from 1956-57 and a Guggenheim Fellow in Zurich in 1967. In 1978, he received the first Carol Karp Prize of the Association for Symbolic Logic for his work on the logic of infinitely long expressions using a technical tool from topology known today as the Vaught transform. This award is the leading international prize for research in mathematical logic, and is awarded only once every five years.

Early in his career, Vaught formulated a fundamental conjecture in model theory long known as "Vaught's Conjecture." Many researchers have tried to prove or disprove this conjecture, and these efforts have led to the development of important new concepts. But the conjecture remains one of the most famous unsolved problems in logic, and is sure to attract further research until it is solved.

Vaught had a long line of distinguished students who wrote their doctoral dissertations under his guidance. One of them, professor James Baumgartner of Dartmouth College, wrote (long after his student days) that "effectiveness" is the bottom line in evaluating teaching, and called Vaught "the most effective mathematics teacher that I have yet encountered."

Vaught's writing was noted for its great clarity, and in 1985 he published a senior-level undergraduate text on set theory that has been described by a reviewer as "impeccable in its precision, thoughtful in its historical and methodological commentary."

Vaught is survived by his wife, Marilyn, of El Cerrito, Calif.; his daughter, Katherine, of Oakland; his son, David, of College Station, Texas; a granddaughter; and his sister, Gail Vaught Searcy, of Berkeley.