Saharon Shelah (; , ; born July 3, 1945) is an Israeli mathematician. He is a professor of
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
at the
Hebrew University of Jerusalem
The Hebrew University of Jerusalem (HUJI; ) is an Israeli public university, public research university based in Jerusalem. Co-founded by Albert Einstein and Chaim Weizmann in July 1918, the public university officially opened on 1 April 1925. ...
and
Rutgers University in
New Jersey
New Jersey is a U.S. state, state located in both the Mid-Atlantic States, Mid-Atlantic and Northeastern United States, Northeastern regions of the United States. Located at the geographic hub of the urban area, heavily urbanized Northeas ...
.
Biography
Shelah was born in
Jerusalem
Jerusalem is a city in the Southern Levant, on a plateau in the Judaean Mountains between the Mediterranean Sea, Mediterranean and the Dead Sea. It is one of the List of oldest continuously inhabited cities, oldest cities in the world, and ...
on July 3, 1945. He is the son of the
Hebrew
Hebrew (; ''ʿÎbrit'') is a Northwest Semitic languages, Northwest Semitic language within the Afroasiatic languages, Afroasiatic language family. A regional dialect of the Canaanite languages, it was natively spoken by the Israelites and ...
poet and
Canaanist political activist
Yonatan 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. 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) is a Public university, public research university in Tel Aviv, Israel. With over 30,000 students, it is the largest university in the country. Located in northwest Tel Aviv, the university is the center of teaching and ...
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 tertiary education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase , which roughly means "community of teachers and scholars". Uni ...
(1977–78), the
University of California, Berkeley
The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...
(1978 and 1982), the
University of Michigan
The University of Michigan (U-M, U of M, or Michigan) is a public university, public research university in Ann Arbor, Michigan, United States. Founded in 1817, it is the oldest institution of higher education in the state. The University of Mi ...
(1984–85), at
Simon Fraser University
Simon Fraser University (SFU) is a Public university, public research university in British Columbia, Canada. It maintains three campuses in Greater Vancouver, respectively located in Burnaby (main campus), Surrey, British Columbia, Surrey, and ...
, Burnaby, British Columbia (1985), and
Rutgers University, New Jersey (1985). He has been a distinguished visiting professor at
Rutgers University since 1986.
Academic career
Shelah's main interests lie in
mathematical logic
Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...
,
model theory
In mathematical logic, model theory is the study of the relationship between theory (mathematical logic), formal theories (a collection of Sentence (mathematical logic), sentences in a formal language expressing statements about a Structure (mat ...
in particular, and in
axiomatic set theory.
In
model theory
In mathematical logic, model theory is the study of the relationship between theory (mathematical logic), formal theories (a collection of Sentence (mathematical logic), sentences in a formal language expressing statements about a Structure (mat ...
, 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 Set (mathematics), 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 mathema ...
, 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
Cardinal or The Cardinal most commonly refers to
* Cardinalidae, a family of North and South American birds
**''Cardinalis'', genus of three species in the family Cardinalidae
***Northern cardinal, ''Cardinalis cardinalis'', the common cardinal of ...
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 upper bound to
van der Waerden's numbers V(C,N). He extended
Arrow's impossibility theorem on voting systems.
Maryanthe Malliaris and Shelah
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.
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 IMU Abacus Medal (known before ...
(1974 invited, 1983 plenary, 1986 plenary)
* The first recipient of the
Erdős Prize, in 1977
* The
Karp Prize of the
Association for Symbolic Logic in 1983
* The
Israel Prize
The Israel Prize (; ''pras israél'') is an award bestowed by the State of Israel, and regarded as the state's highest cultural honor.
History
Prior to the Israel Prize, the most significant award in the arts was the Dizengoff Prize and in Israel ...
, 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, 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 of the European Set Theory Society, joint with
Maryanthe Malliaris, 2017
*
Schock Prize in Logic and Philosophy of the
Royal Swedish Academy of Sciences
The Royal Swedish Academy of Sciences () is one of the Swedish Royal Academies, royal academies of Sweden. Founded on 2 June 1739, it is an independent, non-governmental scientific organization that takes special responsibility for promoting nat ...
, 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 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 logic, f ...
'', College Publications 2009
* ''Classification Theory for
Abstract Elementary Classes 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 logic, f ...
'', Volume 2, College Publications 2009
* ''Cardinal Arithmetic'', Oxford University Press 1994
See also
*
List of Israel Prize recipients
This is an incomplete list of recipients of the Israel Prize from the inception of the Prize in 1953 - 2025.
List
For each year, the recipients are, in most instances, listed in the order in which they appear on the official Israel Prize website ...
References
External links
Archive of Shelah's mathematical papers shelah.logic.at
*
{{DEFAULTSORT:Shelah, Saharon
1945 births
20th-century Israeli mathematicians
21st-century Israeli mathematicians
Einstein Institute of Mathematics alumni
Academic staff of the Hebrew University of Jerusalem
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
Erdős Prize recipients