Saharon Shelah

Shelah was born in Jerusalem on July 3, 1945. He is the son of the Hebrew poet and Canaanist political activist Yonatan Ratosh.{{in lang|he}} {{cite news | url=http://www.haaretz.co.il/misc/1.691997 | title=זיכרונותיו של בן|trans-title=Memoirs of a Son| last=Shelah | first=Saharon | date=April 5, 2001 | newspaper=Haaretz | access-date=August 31, 2014 | quote={{lang|he|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 ...]}} 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.{{in lang|hu}} {{cite web | url=http://www.matud.iif.hu/01mar/shelah.html | title= Harc a matematikával és a titkárnőkkel | language=hu |trans-title=Struggle with mathematics and the secretaries | last=Réka | first=Szász |date=March 2001 | work=Magyar Tudományos | access-date=August 31, 2014 | quote=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.{{cite web |url = http://www.omath.org.il/image/users/112431/ftp/my_files/the_interview.pdf |title = Interview with Saharon Shelah |author = Moshe Klein |publisher= Gan Adam |access-date = 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.{{cite web |url = http://www-history.mcs.st-and.ac.uk/Biographies/Shelah.html |title = Saharon Shelah |publisher =School of Mathematics and Statistics, University of St Andrews, Scotland |access-date = 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.

Shelah's main interests lie in mathematical logic, model theory in particular, and in axiomatic set theory.{{cite journal | last1 = Väänänen | first1 = Jouko | title = An Overview of Saharon Shelah's Contributions to Mathematical Logic, in Particular to Model Theory | journal = Theoria | date = 20 April 2020 | volume = 87 | issue = 2 | pages = 349–360 | issn = 0040-5825 | eissn = 1755-2567 | doi = 10.1111/theo.12238 | pmid = | s2cid = 216119512 | url = | doi-access = free | hdl = 10138/315013 | hdl-access = free }}

In model theory, he developed classification theory, which led him to a solution of Morley's problem.{{cite journal | last1=Hart | first1=Bradd | last2=Hrushovski | first2=Ehud | last3=Laskowski | first3=Michael C. | title=The Uncountable Spectra of Countable Theories | journal=The Annals of Mathematics | volume=152 | issue=1 | date=2000 | doi=10.2307/2661382 | doi-access=free | page=207 | jstor=2661382 | arxiv=math/0007199 }} 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 Jónsson group,{{cite book | last=Shelah | first=Saharon | title=Studies in Logic and the Foundations of Mathematics | chapter=On a Problem of Kurosh, Jonsson Groups, and Applications | publisher=Elsevier | volume=95 | date=1980 | isbn=978-0-444-85343-1 | doi=10.1016/s0049-237x(08)71346-6 | pages=373–394}} an uncountable group for which every proper subgroup is countable. He showed that Whitehead's problem{{cite journal | last=Shelah | first=Saharon | title=Infinite abelian groups, whitehead problem and some constructions | journal=Israel Journal of Mathematics | volume=18 | issue=3 | date=1974 | issn=0021-2172 | doi=10.1007/BF02757281 | pages=243–256}} is independent of ZFC. He gave the first primitive recursive upper bound to van der Waerden's numbers V(C,N).{{cite journal | first=Saharon | last=Shelah | title=Primitive recursive bounds for van der Waerden numbers | journal=Journal of the American Mathematical Society | volume=1 | year=1988 | pages=683–697 | issue=3 | doi=10.2307/1990952 | mr=929498| jstor=1990952 | doi-access=free }} He extended Arrow's impossibility theorem on voting systems.{{cite arXiv | eprint=math/0112213 | last1=Shelah | first1=Saharon | title=On the Arrow property | date=2001 }}

Maryanthe Malliaris and Shelah{{cite journal | last1 = Malliaris | first1 = M. | last2 = Shelah | first2 = S. | doi = 10.1090/jams830 | issue = 1 | journal = Journal of the American Mathematical Society | mr = 3402699 | pages = 237–297 | title = Cofinality spectrum theorems in model theory, set theory, and general topology | volume = 29 | year = 2016| arxiv = 1208.5424 | s2cid = 13182394 }} studied Keisler's order, a construction from model theory, and in the process proved equality between two cardinal characteristics of the continuum, 𝖕 and 𝖙, resolving a problem that had been open for fifty years. This work earned them the 2017 Hausdorff Medal of the European Set Theory Society.

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.{{cite journal | last1 = Zilber | first1 = Boris | title = Model theory of special subvarieties and Schanuel-type conjectures | journal = Annals of Pure and Applied Logic | date = October 2016 | volume = 167 | issue = 10 | pages = 1000–1028 | issn = 0168-0072 | doi = 10.1016/j.apal.2015.02.002 | pmid = | s2cid = 33799837 | url = | doi-access = free | arxiv = 1501.03301 }}

• Three times speaker at the International Congress of Mathematicians (1974 invited, 1983 plenary, 1986 plenary)
• The first recipient of the Erdős Prize, in 1977{{cite web | title = Erdős Prize Website| url = http://imu.org.il/Prizes/ErdosPrize/erdos_prize.html| archive-url = https://web.archive.org/web/20130817024908/http://imu.org.il/Prizes/ErdosPrize/erdos_prize.html| url-status = dead| archive-date = August 17, 2013|publisher=IMU.org.il}}
• The Karp Prize of the Association for Symbolic Logic in 1983{{cite news |title= Karp Prize Recipients | newspaper=Association for Symbolic Logic | url=https://aslonline.org/asl-information/prizes-and-awards/karp-prize-recipients/ |access-date= September 28, 2019}}
• The Israel Prize, for mathematics, in 1998{{cite web | title = Israel Prize Official Site – Recipients in 1998 (in Hebrew)| url = http://cms.education.gov.il/EducationCMS/Units/PrasIsrael/TashnagTashsab/TASNAG_TASNAT_Rikuz.htm?DictionaryKey=Tashnach | publisher=CMS.education.gov.il | access-date=August 31, 2014}}
• The Bolyai Prize in 2000{{cite web | title = Laudation of Shelah on the occasion of winning the Bolyai Prize (in Hungarian)| url = http://www.renyi.hu/~csirmaz/shelah/sh.pdf | publisher=Renyi.hu | access-date=August 31, 2014}}
• The Wolf Prize in Mathematics in 2001{{cite web | title=The Wolf Foundation Prize in Mathematics | url=http://www.wolffund.org.il/index.php?dir=site&page=winners&name=&prize=%D7%91%D7%97%D7%A8+%D7%94%D7%9B%D7%9C&year=2001&field=3004 | publisher=Wolf Foundation | year=2008 | access-date=August 31, 2014 | archive-date=September 21, 2017 | archive-url=https://web.archive.org/web/20170921000823/http://www.wolffund.org.il/index.php?dir=site&page=winners&name=&prize=%D7%91%D7%97%D7%A8+%D7%94%D7%9B%D7%9C&year=2001&field=3004 | url-status=dead }}
• The EMET Prize for Art, Science and Culture in 2011{{cite web | title=EMET Prize | url=http://en.emetprize.org/laureates/exact-sciences/mathematics/prof-saharon-shelah/ | archive-url=https://web.archive.org/web/20140903081809/http://en.emetprize.org/laureates/exact-sciences/mathematics/prof-saharon-shelah/ | url-status=usurped | archive-date=September 3, 2014 | year=2011 | access-date=August 31, 2014}}
• The Leroy P. Steele Prize, for Seminal Contribution to Research, in 2013{{cite web |title=January 2013 Prizes and Awards |date=January 10, 2013 |publisher=American Mathematical Society and Mathematical Association of America |url=http://www.ams.org/profession/prizebooklet-2013.pdf |page=49 |access-date=August 31, 2014}}
• Honorary member of the Hungarian Academy of Sciences, in 2013{{cite web|title=New members of the Hungarian Academy of Sciences |url=http://mta.hu/articles/new-members-of-the-hungarian-academy-of-sciences-131864/ |access-date=August 31, 2014 |url-status=dead |archive-url=https://web.archive.org/web/20140903115610/http://mta.hu/articles/new-members-of-the-hungarian-academy-of-sciences-131864/ |archive-date=September 3, 2014 }}
• Advanced grant of the European Research Council (2013){{cite web | title = ERC Grants 2013 | publisher=European Research Council | url=http://erc.europa.eu/sites/default/files/document/file/erc_2013_adg_results_all_domains.pdf | year=2013 | access-date=August 31, 2014}}
• Hausdorff Medal of the European Set Theory Society, joint with Maryanthe Malliaris, 2017{{cite web |title= Hausdorff medal 2017| url=https://ests.wordpress.com/2017/07/05/third-hausdorff-medal-2017/ |access-date= September 28, 2019| date=July 5, 2017 }}
• Schock Prize in Logic and Philosophy of the Royal Swedish Academy of Sciences, 2018{{cite web|title=Schock Prize 2018|url=https://www.kva.se/en/pressroom/pressmeddelanden/en-matematiker-en-logiker-en-solist-och-en-italiensk-avantgardist-tilldelas-rolf-schockprisen-2018|access-date=September 28, 2019}}
• Honorary doctorate from the Technische Universität Wien, 2019{{cite web|title=Ehrendoktorat der TU Wien für Saharon Shelah|url=https://www.tuwien.at/tu-wien/aktuelles/news/news/ehrendoktorat-der-tu-wien-fuer-saharon-shelah/|access-date=February 2, 2020|year=2019}}

• Proper forcing, Springer 1982 {{ISBN|978-0-387-11593-1}}
• Proper and improper forcing (2nd edition of Proper forcing), Springer 1998 {{ISBN|978-1107168367}}
• Around classification theory of models, Springer 1986 {{ISBN|978-3540164487}}
• Classification theory and the number of non-isomorphic models, Studies in Logic and the Foundations of Mathematics, 1978,{{cite journal|author=Baldwin, John T.|title=Review: Classification theory and the number of non-isomorphic models by Saharon Shelah|journal=Bull. Amer. Math. Soc. (N.S.)|year=1981|volume=4|issue=2|pages=222–229|url=http://www.ams.org/journals/bull/1981-04-02/S0273-0979-1981-14891-6/S0273-0979-1981-14891-6.pdf|doi=10.1090/s0273-0979-1981-14891-6|doi-access=free}} [https://books.google.com/books/about/Classification_Theory.html?id=5pwf8DGNHckC 2nd edition 1990], Elsevier {{ISBN|978-0-444-70260-9}}
• Classification Theory for Abstract Elementary Classes, College Publications 2009 {{ISBN|9781904987710}}
• Classification Theory for Abstract Elementary Classes, Volume 2, College Publications 2009 {{ISBN|978-1-904987-72-7}}
• Cardinal Arithmetic, Oxford University Press 1994 {{ISBN|0-19-853785-9}}{{cite journal|author=Baumgartner, James E.|author-link=James Earl Baumgartner|title=Review: Cardinal arithmetic by Saharon Shelah|journal=Bull. Amer. Math. Soc. (N.S.)|year=1996|volume=33|issue=3|pages=409–411|url=http://www.ams.org/journals/bull/1996-33-03/S0273-0979-96-00673-8/S0273-0979-96-00673-8.pdf|doi=10.1090/s0273-0979-96-00673-8|doi-access=free}}

• List of Israel Prize recipients

{{Reflist|colwidth=30em}}

{{Scholia}}

• [http://shelah.logic.at/ Archive of Shelah's mathematical papers], shelah.logic.at
• {{cite book |last=Baldwin |first=John T.| editor-last=Andretta | editor-first=Alessandro | editor-last2=Kearnes | editor-first2=Keith | editor-last3=Zambella | editor-first3=Domenico | title=Logic Colloquium 2004|chapter= Abstract elementary classes: some answers, more questions| publisher=Cambridge University Press | publication-place=Chicago, IL : Cambridge | date=2008 | isbn=978-0-521-88424-2 | oclc=177021884|pages=1–17}}

{{Wolf Prize in Mathematics}}

{{Schock Prize laureates}}

{{Authority control}}

{{DEFAULTSORT:Shelah, Saharon}}

Category:1945 births

Category:20th-century Israeli mathematicians

Category:21st-century Israeli mathematicians

Category:Einstein Institute of Mathematics alumni

Category:Academic staff of the Hebrew University of Jerusalem

Category:Israel Prize in mathematics recipients

Category:Israeli Jews

Category:Jewish scientists

Category:Living people

Category:Members of the Hungarian Academy of Sciences

Category:Members of the Israel Academy of Sciences and Humanities

Category:Model theorists

Category:Rutgers University faculty

Category:Set theorists

Category:Wolf Prize in Mathematics laureates

Category:European Research Council grantees

Category:Hausdorff Medal winners

Category:Erdős Prize recipients