Saharon Shelah ( he, שהרן שלח; born July 3, 1945) is an Israeli mathematician. He is a professor of

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

at the

Hebrew University of Jerusalem The Hebrew University of Jerusalem (HUJI; he, הַאוּנִיבֶרְסִיטָה הַעִבְרִית בִּירוּשָׁלַיִם) is a public research university based in Jerusalem, Israel. Co-founded by Albert Einstein and Dr. Chaim Weiz ...

and

Rutgers University Rutgers University (; RU), officially Rutgers, The State University of New Jersey, is a Public university, public land-grant research university consisting of four campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's ...

New Jersey New Jersey is a state in the Mid-Atlantic and Northeastern regions of the United States. It is bordered on the north and east by the state of New York; on the east, southeast, and south by the Atlantic Ocean; on the west by the Delaware ...

Biography

Shelah was born in

Jerusalem Jerusalem (; he, יְרוּשָׁלַיִם ; ar, القُدس ) (combining the Biblical and common usage Arabic names); grc, Ἱερουσαλήμ/Ἰεροσόλυμα, Hierousalḗm/Hierosóluma; hy, Երուսաղեմ, Erusałēm. i ...

on July 3, 1945. He is the son of the Israeli poet and political activist

Yonatan Ratosh Yonatan Ratosh () was the literary pseudonym of Uriel Shelach ( he, אוריאל שלח) (November 18, 1908 – March 25, 1981), an Israeli poet and journalist who founded the Canaanite movement. Biography Uriel Heilperin (later Shelach) was ...

. 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. His brother, magistrate judge Hamman Shelah was murdered along with his wife and daughter by an Egyptian soldier in the

Ras Burqa massacre The Ras Burqa massacre was a mass shooting on 5 October 1985 on Israeli vacationers in Ras Burqa, a beach resort area in the Sinai peninsula, in which seven, including four children, were killed by Egyptian soldier Suleiman Khater. The at ...

in 1985. 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 Tel Aviv University (TAU) ( he, אוּנִיבֶרְסִיטַת תֵּל אָבִיב, ''Universitat Tel Aviv'') is a public research university in Tel Aviv, Israel. With over 30,000 students, it is the largest university in the country. Locate ...

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 A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, t ...

(1977–78), the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

(1978 and 1982), the

University of Michigan , mottoeng = "Arts, Knowledge, Truth" , former_names = Catholepistemiad, or University of Michigania (1817–1821) , budget = $10.3 billion (2021) , endowment = $17 billion (2021)As o ...

(1984–85), at

Simon Fraser University Simon Fraser University (SFU) is a public research university in British Columbia, Canada, with three campuses, all in Greater Vancouver: Burnaby (main campus), Surrey, and Vancouver. The main Burnaby campus on Burnaby Mountain, located from ...

, Burnaby, British Columbia (1985), and

, New Jersey (1985). He has been a distinguished visiting professor at

since 1986.

Academic career

Shelah's personal webpage, lists 1108 published mathematical papers, as well as more than 100 preprints and papers in preparation, including joint papers with 260 co-authors; the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

's database

MathSciNet MathSciNet is a searchable online bibliographic database created by the American Mathematical Society in 1996. It contains all of the contents of the journal ''Mathematical Reviews'' (MR) since 1940 along with an extensive author database, links ...

lists 1063 published books and journal articles with 248 coauthors. His main interests lie in

mathematical logic Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of for ...

model theory In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the s ...

in particular, and in axiomatic set theory. In

, he developed ''classification theory'', which led him to a solution of Morley's problem. In

set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly conce ...

, 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 In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states that or equivalently, that In Zermelo–Fraenkel set theory with the axiom of choice (ZFC), this is equivalent to ...

), there are still highly nontrivial ZFC theorems about cardinal exponentiation. Shelah constructed a Jónsson 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 In computability theory, a primitive recursive function is roughly speaking a function that can be computed by a computer program whose loops are all "for" loops (that is, an upper bound of the number of iterations of every loop can be determined ...

upper bound to van der Waerden's numbers V(C,N). He extended

Arrow's impossibility theorem Arrow's impossibility theorem, the general possibility theorem or Arrow's paradox is an impossibility theorem in social choice theory that states that when voters have three or more distinct alternatives (options), no ranked voting electoral syst ...

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 Ehud Hrushovski ( he, אהוד הרושובסקי; born 30 September 1959) is a mathematical logician. He is a Merton Professor of Mathematical Logic at the University of Oxford and a Fellow of Merton College, Oxford. He was also Professor of ...

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 Boris Zilber (russian: Борис Иосифович Зильбер, born 1949) is a Soviet-British mathematician who works in mathematical logic, specifically model theory. He is a professor of mathematical logic at the University of Oxford. ...

Awards

* Three times speaker at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

(1974 invited, 1983 plenary, 1986 plenary) * The first recipient of the

Erdős Prize The Anna and Lajos Erdős Prize in Mathematics is a prize given by the Israel Mathematical Union to an Israeli mathematician (in any field of mathematics and computer science), "with preference to candidates up to the age of 40." The prize was e ...

, in 1977 * The

Karp Prize The Association for Symbolic Logic (ASL) is an international organization of specialists in mathematical logic and philosophical logic. The ASL was founded in 1936, and its first president was Alonzo Church. The current president of the ASL is ...

of the

Association for Symbolic Logic The Association for Symbolic Logic (ASL) is an international organization of specialists in mathematical logic and philosophical logic. The ASL was founded in 1936, and its first president was Alonzo Church. The current president of the ASL is ...

in 1983 * The

Israel Prize The Israel Prize ( he, פרס ישראל; ''pras israél'') is an award bestowed by the State of Israel, and regarded as the state's highest cultural honor. History The Israel Prize is awarded annually, on Israeli Independence Day, in a state cer ...

, for mathematics, in 1998 * The

Bolyai Prize The International János Bolyai Prize of Mathematics is an international prize founded by the Hungarian Academy of Sciences. The prize is named after János Bolyai and is awarded every five years to mathematicians for monographs with important new r ...

in 2000 * The Wolf Prize in Mathematics in 2001 *

The EMET Prize for Art, Science and Culture ''The'' () is a grammatical article in English, denoting persons or things already mentioned, under discussion, implied or otherwise presumed familiar to listeners, readers, or speakers. It is the definite article in English. ''The'' is the m ...

in 2011 * The

Leroy P. Steele Prize The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories. The prizes have b ...

, for Seminal Contribution to Research, in 2013 * Honorary member of the Hungarian Academy of Sciences, in 2013 * Advanced grant of the

European Research Council The European Research Council (ERC) is a public body for funding of scientific and technological research conducted within the European Union (EU). Established by the European Commission in 2007, the ERC is composed of an independent Scientific ...

(2013) *

Hausdorff Medal The Hausdorff medal is a mathematical prize awarded every two years by the European Set Theory Society. The award recognises the work considered to have had the most impact within set theory among all articles published in the previous five years. ...

of the European Set Theory Society, joint with

Maryanthe Malliaris Maryanthe Elizabeth Malliaris is a professor of mathematics at the University of Chicago, a specialist in model theory. Early life and education Malliaris is the daughter of Anastasios G. (Tassos) Malliaris, an economist at Loyola University Chi ...

, 2017 *

Schock Prize The Rolf Schock Prizes were established and endowed by bequest of philosopher and artist Rolf Schock (1933–1986). The prizes were first awarded in Stockholm Stockholm () is the capital and largest city of Sweden as well as the largest ...

in Logic and Philosophy of the Royal Swedish Academy of Sciences, 2018 *

Honorary doctorate An honorary degree is an academic degree for which a university (or other degree-awarding institution) has waived all of the usual requirements. It is also known by the Latin phrases ''honoris causa'' ("for the sake of the honour") or ''ad hon ...

from the

Technische Universität Wien TU Wien (TUW; german: Technische Universität Wien; still known in English as the Vienna University of Technology from 1975–2014) is one of the major universities in Vienna, Austria. The university finds high international and domestic recogn ...

, 2019

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
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 1994

References

External links