Robert M. Solovay

Robert M. Solovay
George M. Bergman · GFDL 1.2 · source
Name	Robert M. Solovay
Birth date	1938
Birth place	New York City
Nationality	United States
Fields	Mathematics
Alma mater	Harvard University, University of California, Berkeley
Doctoral advisor	Alfred Tarski
Known for	Solovay model, Solovay functions, work on set theory, measure theory, real analysis

Robert M. Solovay (born 1938) is an American mathematician noted for foundational work in set theory, measure theory, and the interaction between axiomatic set theory and real analysis. His constructions and independence results influenced research at institutions such as Harvard University, University of California, Berkeley, and Institute for Advanced Study, and informed later developments by figures including Kurt Gödel, Paul Cohen, and Dana Scott. Solovay's work on models of Zermelo–Fraenkel set theory with the Axiom of Choice omitted reshaped perspectives on measurable sets and definability in descriptive set theory.

Early life and education

Solovay was born in New York City and raised in a period shaped by post-World War II American scientific expansion and the rise of modern mathematics in North American universities. He completed undergraduate study at Harvard University, where he encountered faculty such as Alfred Tarski and peers influenced by logicians from Princeton University and the University of Chicago. For graduate study he attended the University of California, Berkeley, working in an environment connected to scholars at Massachusetts Institute of Technology and research groups with ties to Institute for Advanced Study and Bryn Mawr College. His doctoral work under Alfred Tarski placed him in the lineage of twentieth-century logicians that included Kurt Gödel and Stanislaw Ulam.

Academic career

Solovay held academic appointments at institutions including Princeton University, where he interacted with researchers from Bell Labs and colleagues connected to the University of Pennsylvania and Yale University. Later positions included roles at Brown University and visiting fellowships at Institute for Advanced Study and exchange visits to University of California, Los Angeles and University of Oxford. He collaborated with mathematicians from Harvard University, Massachusetts Institute of Technology, and Columbia University and supervised students who went on to positions at University of Michigan, Rutgers University, and University of California, Berkeley.

Research and contributions

Solovay's most celebrated contribution is the construction of the Solovay model, a model of Zermelo–Fraenkel set theory (ZF) without the Axiom of Choice in which every set of real numbers is Lebesgue measure-measurable, has the property of Baire, and satisfies the perfect set property. That result built on earlier work by Kurt Gödel on constructible universes and by Paul Cohen on forcing, drawing techniques related to the Levy collapse and interactions with large cardinal hypotheses such as the inaccessible cardinal. His use of forcing and inner model theory influenced contemporaries including Azriel Lévy and later researchers like Hugh Woodin and W. Hugh Woodin in investigations of determinacy principles and projective determinacy. Solovay also developed what are often called Solovay functions in the study of definability and combinatorial set theory, contributing to the understanding of ordinal definability, the constructible universe, and admissible sets as studied by Gerald Sacks and Dana Scott.

Beyond foundational models, Solovay made substantive contributions to the theory of measurable cardinals and the interaction between large cardinals and real-valued measurable cardinals, advancing themes pursued by Kurt Gödel and John von Neumann. His results clarified how hypotheses about large cardinals affect regularity properties of sets of reals and informed applications to descriptive set theory topics studied by Yiannis N. Moschovakis and Donald A. Martin. Collaborations and exchanges with logicians at Carnegie Mellon University, University of California, Berkeley, and Northwestern University helped disseminate techniques combining forcing, inner models, and combinatorial set theory.

Solovay's work is characterized by rigorous use of techniques from forcing (mathematics), inner model theory, and measure-theoretic methods, interfacing with the research traditions of Princeton University logicians and the European set-theory schools centered at Paris Diderot University and Universität Münster.

Selected publications

- “A Model of Set‑Theory in Which Every Set of Reals Is Lebesgue Measurable,” (landmark paper) published in proceedings and reprinted in collections alongside work by Paul Cohen and Kurt Gödel. - Papers on combinatorial set theory and definability, appearing in journals alongside contributions by Dana Scott, Gerald Sacks, and Azriel Lévy. - Expository and survey articles on forcing and the role of large cardinals, cited in works by Hugh Woodin and Donald A. Martin.

Honors and recognition

Solovay received recognition within the mathematics community through invited lectures at venues such as International Congress of Mathematicians, colloquia at Institute for Advanced Study, and honors from organizations including the American Mathematical Society and regional societies linked to Harvard University and University of California, Berkeley. His results are standard material in advanced treatments of set theory and are frequently cited in monographs by authors like Kenneth Kunen and Thomas Jech, and in surveys by Yiannis N. Moschovakis.

Category:Set theorists Category:1938 births Category:Living people