Saharon Shelah, "Rutgers University, 2005
July 3, 1945 |
"Jerusalem, "British Mandate for Palestine
|Alma mater||Tel Aviv University (B.Sc)
Hebrew University (M.Sc.)
Hebrew University (Ph.D.)
|Known for||"Mathematical logic, "model theory, "set theory|
|Awards||"Erdős Prize (1977)
Rothschild Prize (1982)
"Karp Prize (1983)
"George Pólya Prize (1992)
"Bolyai Prize (2000)
"Wolf Prize (2001)
"Israel Prize (1998)
"EMET Prize (2011)
"Leroy P. Steele Prize (2013)
|Institutions||"Hebrew University, "Rutgers University|
|"Doctoral advisor||"Michael O. Rabin|
|Doctoral students||"Rami Grossberg|
Shelah was born in "Jerusalem on July 3, 1945. He is the son of the Israeli poet and political activist "Yonatan Ratosh. He received his PhD for his work on stable theories in 1969 from the Hebrew University.
Shelah planned to be a scientist while at primary school, but initially was attracted to physics and biology, not mathematics. Later he found "mathematical beauty in studying geometry: He said, "But when I reached the ninth grade I began studying geometry and my eyes opened to that beauty—a system of demonstration and theorems based on a very small number of axioms which impressed me and captivated me." At the age of 15, he decided to become a mathematician, a choice cemented after reading "Abraham Halevy Fraenkel's book "An Introduction to Mathematics".
He received a B.Sc. from Tel Aviv University in 1964, served in the Israel Defense Forces Army between 1964 and 1967, and obtained a M.Sc. from the Hebrew University (under the direction of Haim Gaifman) in 1967. He then worked as a Teaching Assistant at the Institute of Mathematics of the Hebrew University of Jerusalem while completing a Ph.D. there under the supervision of "Michael Oser Rabin, on a study of stable theories.
Shelah was a Lecturer at Princeton University during 1969-70, and then worked as an Assistant Professor at the University of California, Los Angeles during 1970-71. He became a professor at Hebrew University in 1974, a position he continues to hold.
He has been a Visiting Professor at the following Universities: the "University of Wisconsin (1977–78), the "University of California, Berkeley (1978 and 1982), the "University of Michigan (1984–85), at "Simon Fraser University, Burnaby, "British Columbia (1985), and "Rutgers University, New Jersey (1985).
Shelah's archive, as of September 2017[update] lists 1124 mathematical papers including joint papers with over 220 co-authors. His main interests lie in "mathematical logic, "model theory in particular, and in "axiomatic set theory.
In "model theory, he developed classification theory, which led him to a solution of "Morley's problem. In "set theory, he discovered the notion of "proper forcing, an important tool in iterated "forcing arguments. With "PCF theory, he showed that in spite of the undecidability of the most basic questions of cardinal arithmetic (such as the "continuum hypothesis), there are still highly nontrivial "ZFC theorems about "cardinal exponentiation. Shelah constructed a Jonsson group, an uncountable group for which every proper subgroup is countable. He showed that "Whitehead's problem is "independent of ZFC. He gave the first "primitive recursive upper bound to "van der Waerden's numbers V(C,N). He extended "Arrow's impossibility theorem on voting systems.
Shelah's work has had a deep impact on model theory and set theory. The tools he developed for his classification theory have been applied to a wide number of topics and problems in model theory and have led to great advances in stability theory and its uses in algebra and algebraic geometry as shown for example by "Ehud Hrushovski and many others. Classification theory involves deep work developed in many dozens of papers to completely solve the spectrum problem on classification of first order theories in terms of structure and number of nonisomorphic models, a huge tour de force. Following that he has extended the work far beyond first order theories, for example for "Abstract Elementary Classes. This work also has had important applications to algebra by works of "Boris Zilber.
כשעמדתי להציג לפני חברתי יעל (עתה רעייתי) את בני משפחתי...הפרופ' שהרן שלח מן האוניברסיטה העברית בירושלים, בנו של יונתן רטוש... [As I was about to present to friend Yael (now my wife), my family ... Professor Saharon Shelah of the Hebrew University of Jerusalem, son of Yonathan Ratosh ...]
Hungarian: A gyerekei mivel foglalkoznak? A nagyobbik fiam zeneelméletet tanul, a lányom történelmet, a kisebbik fiam pedig biológiát. (What are your children doing? My elder son is learning the theory of music, my daughter history, my younger son biology.)