Saharon Shelah

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Saharon Shelah
Saharon Shelah in his office in Rutgers University, September 6, 2005. Photo by Andrzej Rosłanowski.
Born (1945-07-03) July 3, 1945 (age 74)
Jerusalem, British Mandate for Palestine
Residence Jerusalem, Israel
Nationality Israel
Fields Mathematics
Institutions Hebrew University, Rutgers University
Alma mater Tel Aviv University (B.Sc)
Tel Aviv University (M.Sc.)
Hebrew University (Ph.D.)
Doctoral advisor Michael O. Rabin
Doctoral students Uri Abraham, Shai Ben-David, Rami Grossberg, Menachem Kojman, Mati Rubin[1]
Known for Mathematical logic, model theory, set theory
Notable awards Erdős Prize (1977)
George Pólya Prize (1992)
Bolyai Prize (2000)
Wolf Prize (2001)
Israel Prize (1998)
Leroy P. Steele Prize (2013)

Saharon Shelah (Hebrew: שהרן שלח‎) is an Israeli mathematician. He is a professor of mathematics at the Hebrew University of Jerusalem and Rutgers University in New Jersey.


Shelah was born in Jerusalem on July 3, 1945. He is the son of the Israeli poet and political activist Yonatan Ratosh.[2] He received his PhD for his work on stable theories in 1969 from the Hebrew University.[1]

Shelah is married to Yael,[2] and has three children.[3]

Shelah wanted to be a scientist while at primary school, but initially was attracted to physics and biology, not mathematics.[4] 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".[4]

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 Tel Aviv University in 1967.[5] 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,[5] 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.[5] He became a professor at Hebrew University in 1974, a position he continues to hold.[5]

He has been a Visiting Professor at the following Universities:[5] 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.[5]

Academic career

According to the list of Shelah's papers, he had published 1044 mathematical papers up to 2014 (including joint papers with over 220 co-authors).[6] 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 Kurosh monster, 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.


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,[15] 2nd edition 1990, Elsevier
  • Cardinal Arithmetic, Oxford University Press 1994[16]

See also


  1. 1.0 1.1 Saharon Shelah at the Mathematics Genealogy Project
  2. 2.0 2.1 (Hebrew) Shelah, Saharon (2001-04-05). "זיכרונותיו של בן" [Memoirs of a Son]. Haaretz. Retrieved 2014-08-31. 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 ...]<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  3. (Hungarian) Réka, Szász (March 2001). "Harc a matematikával és a titkárnőkkel". Magyar Tudományos (in magyar). Retrieved 2014-08-31. 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.) Unknown parameter |trans_title= ignored (help)<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  4. 4.0 4.1 Moshe Klein. "Interview with Saharon Shelah" (PDF). Gan Adam. Retrieved 2014-08-05.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  5. 5.0 5.1 5.2 5.3 5.4 5.5 "Saharon Shelah". School of Mathematics and Statistics, University of St Andrews, Scotland. Retrieved 2014-08-05.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  6. "Hyperlinked list of Shelah's papers". Retrieved 2014-08-05.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  7. "Erdős Prize Website".<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  8. "Israel Prize Official Site – Recipients in 1998 (in Hebrew)". Retrieved 2014-08-31.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  9. "Laudation of Shelah on the occasion of winning the Bolyai Prize (in Hungarian)" (PDF). Retrieved 2014-08-31.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  10. "The Wolf Foundation Prize in Mathematics". Wolf Foundation. 2008. Retrieved 2014-08-31.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  11. "EMET Prize". 2011. Retrieved 2014-08-31.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  12. "January 2013 Prizes and Awards" (PDF). American Mathematical Society and Mathematical Association of America. January 10, 2013. p. 49. Retrieved 2014-08-31.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  13. "New members of the Hungarian Academy of Sciences". Retrieved 2014-08-31.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  14. "ERC Grants 2013" (PDF). European Research Council. 2013. Retrieved 2014-08-31.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  15. Lua error in Module:Citation/CS1/Identifiers at line 47: attempt to index field 'wikibase' (a nil value).
  16. Lua error in Module:Citation/CS1/Identifiers at line 47: attempt to index field 'wikibase' (a nil value).

External links