Saharon Shelah

Saharon Shelah (Template:Langx; Template:Transliteration, Template:IPA; 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 Hebrew poet and Canaanist political activist Yonatan Ratosh.<ref name="Memoir">Template:In lang Template:Cite news</ref> He attended Tichon Hadash high school in Tel Aviv.<ref>Template:Cite web</ref> He received his PhD for his work on stable theories in 1969 from the Hebrew University.<ref name="mg" />

Shelah is married to Yael,<ref name = "Memoir" /> and has three children.<ref>Template:In lang Template:Cite web</ref> 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.<ref name="interview">Template:Cite web</ref> 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.<ref name="interview" />

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.<ref name="mactutor">Template:Cite web</ref> 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,<ref name="mactutor" /> 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.<ref name="mactutor" /> He became a professor at Hebrew University in 1974, a position he continues to hold.<ref name="mactutor" />

He has been a visiting professor at the following universities:<ref name="mactutor" /> 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.<ref name="mactutor" />

Academic career

Shelah's main interests lie in mathematical logic, model theory in particular, and in axiomatic set theory.<ref name="Väänänen2020">Template:Cite journal</ref> He is a prolific author, with more than 1100 peer-reviewed research papers since his first in 1969.<ref name="shelah-archive">Template:Cite web</ref>

In model theory, he developed classification theory, which led him to a solution of Morley's problem.<ref name="MorleyShelahSpectra">Template:Cite journal</ref> 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,<ref name="JonssonGroups">Template:Cite book</ref> an uncountable group for which every proper subgroup is countable. He showed that Whitehead's problem<ref name="WhiteheadProblem">Template:Cite journal</ref> is independent of ZFC. He gave the first primitive recursive upper bound to van der Waerden's numbers V(C,N).<ref>Template:Cite journal</ref> He extended Arrow's impossibility theorem on voting systems.<ref>Template:Cite arXiv</ref>

Maryanthe Malliaris and Shelah<ref name=MalliarisShelah>Template:Cite journal</ref> 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.<ref name="Zilber2016">Template:Cite journal</ref>

Awards

• Three times speaker at the International Congress of Mathematicians (1974 invited, 1983 plenary, 1986 plenary)
• The first recipient of the Erdős Prize, in 1977<ref>Template:Cite web</ref>
• The Karp Prize of the Association for Symbolic Logic in 1983<ref>Template:Cite news</ref>
• The Israel Prize, for mathematics, in 1998<ref>Template:Cite web</ref>
• The Bolyai Prize in 2000<ref>Template:Cite web</ref>
• The Wolf Prize in Mathematics in 2001<ref>Template:Cite web</ref>
• The EMET Prize for Art, Science and Culture in 2011<ref>Template:Cite web</ref>
• The Leroy P. Steele Prize, for Seminal Contribution to Research, in 2013<ref>Template:Cite web</ref>
• Honorary member of the Hungarian Academy of Sciences, in 2013<ref>Template:Cite web</ref>
• Advanced grant of the European Research Council (2013)<ref>Template:Cite web</ref>
• Hausdorff Medal of the European Set Theory Society, joint with Maryanthe Malliaris, 2017<ref>Template:Cite web</ref>
• Schock Prize in Logic and Philosophy of the Royal Swedish Academy of Sciences, 2018<ref>Template:Cite web</ref>
• Honorary doctorate from the Technische Universität Wien, 2019<ref>Template:Cite web</ref>

Selected works

• Proper forcing, Springer 1982 Template:ISBN
• Proper and improper forcing (2nd edition of Proper forcing), Springer 1998 Template:ISBN
• Around classification theory of models, Springer 1986 Template:ISBN
• Classification theory and the number of non-isomorphic models, Studies in Logic and the Foundations of Mathematics, 1978,<ref>Template:Cite journal</ref> 2nd edition 1990, Elsevier Template:ISBN
• Classification Theory for Abstract Elementary Classes, College Publications 2009 Template:ISBN
• Classification Theory for Abstract Elementary Classes, Volume 2, College Publications 2009 Template:ISBN
• Cardinal Arithmetic, Oxford University Press 1994 Template:ISBN<ref>Template:Cite journal</ref>

See also

• List of Israel Prize recipients

External links

• Archive of Shelah's mathematical papers, shelah.logic.at
• Template:Cite book