Saharon Shelah ( he, שהרן שלח; born July 3, 1945) is an Israeli mathematician. He is a professor of
mathematics at the
Hebrew University of Jerusalem and
Rutgers University
Rutgers University (; RU), officially Rutgers, The State University of New Jersey, is a public land-grant research university consisting of four campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's College, and wa ...
in
New Jersey
New Jersey is a U.S. state, state in the Mid-Atlantic States, Mid-Atlantic and Northeastern United States, Northeastern regions of the United States. It is bordered on the north and east by the state of New York (state), New York; on the ea ...
.
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 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. ''University'' is derived from the Latin phrase ''universitas magistrorum et scholarium'', which ...
(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 ...
, Burnaby, British Columbia (1985), and
Rutgers University
Rutgers University (; RU), officially Rutgers, The State University of New Jersey, is a public land-grant research university consisting of four campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's College, and wa ...
, New Jersey (1985). He has been a distinguished visiting professor at
Rutgers University
Rutgers University (; RU), officially Rutgers, The State University of New Jersey, is a public land-grant research university consisting of four campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's College, and wa ...
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 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 formal ...
,
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 ...
in particular, and in
axiomatic 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 concern ...
.
In
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 ...
, 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 concer ...
, he discovered the notion of
proper forcing In the mathematical field of set theory, the proper forcing axiom (''PFA'') is a significant strengthening of Martin's axiom, where forcings with the countable chain condition (ccc) are replaced by proper forcings.
Statement
A forcing or par ...
, an important tool in iterated
forcing
Forcing may refer to: Mathematics and science
* Forcing (mathematics), a technique for obtaining independence proofs for set theory
*Forcing (recursion theory), a modification of Paul Cohen's original set theoretic technique of forcing to deal with ...
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 ...
), there are still highly nontrivial
ZFC theorems about
cardinal exponentiation. Shelah constructed a
Jónsson group Jónsson is a surname of Icelandic origin, meaning ''son of Jón''. In Icelandic names, the name is not strictly a surname, but a patronymic. The name refers to:
*Arnar Jónsson (actor) (born 1943), Icelandic actor
*Arnar Jónsson (basketball) (bo ...
, an uncountable group for which every proper subgroup is countable. He showed that
Whitehead's problem
In group theory, a branch of abstract algebra, the Whitehead problem is the following question:
Saharon Shelah proved that Whitehead's problem is independent of ZFC, the standard axioms of set theory.
Refinement
Assume that ''A'' is an abel ...
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
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 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 class In model theory, a discipline within mathematical logic, an abstract elementary class, or AEC for short, is a class of models with a partial order similar to the relation of an elementary substructure of an elementary class in first-order model th ...
es. This work also has had important applications to algebra by works of
Boris Zilber.
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, in 1977
* The
Karp Prize 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, for mathematics, in 1998
* The
Bolyai Prize in 2000
* The
Wolf Prize in Mathematics in 2001
*
The EMET Prize for Art, Science and Culture in 2011
* The
Leroy P. Steele Prize, for Seminal Contribution to Research, in 2013
* Honorary member of the
Hungarian Academy of Sciences
The Hungarian Academy of Sciences ( hu, Magyar Tudományos Akadémia, MTA) is the most important and prestigious learned society of Hungary. Its seat is at the bank of the Danube in Budapest, between Széchenyi rakpart and Akadémia utca. Its mai ...
, 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 Scientif ...
(2013)
*
Hausdorff Medal of the European Set Theory Society, joint with
Maryanthe Malliaris, 2017
*
Schock Prize in Logic and Philosophy of the
Royal Swedish Academy of Sciences, 2018
*
Honorary doctorate from the
Technische Universität Wien, 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
See also
*
List of Israel Prize recipients
This is a complete list of recipients of the Israel Prize from the inception of the Prize in 1953 through to 2022.
List
For each year, the recipients are, in most instances, listed in the order in which they appear on the official Israel Prize ...
References
External links
Archive of Shelah's mathematical papers shelah.logic.at
* A survey of recent work on AECs.
{{DEFAULTSORT:Shelah, Saharon
1945 births
20th-century Israeli mathematicians
21st-century Israeli mathematicians
Einstein Institute of Mathematics alumni
Hebrew University of Jerusalem faculty
Israel Prize in mathematics recipients
Israeli Jews
Jewish scientists
Living people
Members of the Hungarian Academy of Sciences
Members of the Israel Academy of Sciences and Humanities
Model theorists
Rutgers University faculty
Set theorists
Wolf Prize in Mathematics laureates
European Research Council grantees
Hausdorff Medal winners
Gödel Lecturers
Erdős Prize recipients