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Saharon Shelah

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Saharon Shelah
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{{Short description|Israeli mathematician}}{{Use mdy dates|date=September 2019}}







factoids
Jerusalem, Mandatory Palestine>British Mandate for Palestine| residence = Jerusalem, Israel| nationality = IsraelMathematical logic, model theory, axiomatic set theory>set theory| work_institution = Hebrew University, Rutgers University| alma_mater = Tel Aviv University (B.Sc)Hebrew University (M.Sc.) Hebrew University (Ph.D.)| doctoral_advisor = Michael O. RabinRami Grossberg{{MathGenealogy>id=22575}}| known_for = Sauer–Shelah lemma, Shelah cardinalErdős Prize {{small>(1977)}} Rothschild Prize {{smallKarp Prize {{small>(1983)}}George Pólya Prize {{smallBolyai Prize {{small>(2000)}}Wolf Prize in Mathematics {{small>(2001)}}Israel Prize {{smallEMET Prize {{small>(2011)}}Leroy P. Steele Prize {{smallRolf Schock Prizes {{small>(2018)}}| footnotes = }}Saharon Shelah (; born July 3, 1945) is an Israeli mathematician. He is a professor of mathematics at the Hebrew University of Jerusalem and Rutgers University in New Jersey.

Biography

Shelah was born in Jerusalem on July 3, 1945. He is the son of the Israeli poet and political activist Yonatan Ratosh.{{he icon}} NEWS,weblink זיכרונותיו של בן, Memoirs of a Son, Shelah, Saharon, April 5, 2001, Haaretz, August 31, 2014, [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 ...], He received his PhD for his work on stable theories in 1969 from the Hebrew University.Shelah is married to Yael, and has three children.{{hu icon}} WEB,weblink Harc a matematikával és a titkárnőkkel, hu, Struggle with mathematics and the secretaries, Réka, Szász, March 2001, Magyar Tudományos, August 31, 2014, 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.), His brother, magistrate judge Hamman Shelah was murdered along with his wife and daughter by an Egyptian soldier in the Ras Burqa massacre in 1985.Shelah planned to be a scientist while at primary school, but initially was attracted to physics and biology, not mathematics.WEB,weblink Interview with Saharon Shelah, Moshe Klein, Gan Adam, August 5, 2014, 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.WEB,weblink Saharon Shelah, School of Mathematics and Statistics, University of St Andrews, Scotland, August 5, 2014, 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). He has been a Distinguished Visiting Professor at Rutgers University since 1986.

Academic career

Shelah's personal webpage, {{as of|2019|July|lc = yes}} lists 1166 mathematical papers, preprints and papers in preparation, including joint papers with 260 co-authors;WEB,weblink Hyperlinked list of Shelah's papers, August 5, 2014, the American Mathematical Society's database MathSciNet lists 1063 published books and journal articles with 248 coauthors. His main interests lie in mathematical logic, model theory in particular, and in axiomatic set theory.{{citation needed|date=September 2019}}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.{{citation needed|date=September 2019}}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.{{citation needed|date=September 2019}}

Awards

Selected works

  • Proper forcing, Springer 1982
  • Proper and improper forcing (2nd edition of Proper forcing), Springer 1998
  • Around classification theory of models, Springer 1986
  • Classification theory and the number of non-isomorphic models, Studies in Logic and the Foundations of Mathematics, 1978,JOURNAL, Baldwin, John T., Review: Classification theory and the number of non-isomorphic models by Saharon Shelah, Bull. Amer. Math. Soc. (N.S.), 1981, 4, 2, 222–229,weblink 10.1090/s0273-0979-1981-14891-6, 2nd edition 1990, Elsevier
  • Classification Theory for Abstract Elementary Classes, College Publications 2009.
  • Classification Theory for Abstract Elementary Classes, Volume 2, College Publications 2009.
  • Cardinal Arithmetic, Oxford University Press 1994JOURNAL, Baumgartner, James E., James Earl Baumgartner, Review: Cardinal arithmetic by Saharon Shelah, Bull. Amer. Math. Soc. (N.S.), 1996, 33, 3, 409–411,weblink 10.1090/s0273-0979-96-00673-8,

See also

References

{{Reflist|colwidth=30em}}

External links

{{Wolf Prize in Mathematics}}{{Schock Prize laureates}}{{Authority control}}

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