Saharon Shelah
Encyclopedia
Saharon Shelah (1945 - ) is an Israel
i mathematician
. He is a professor of mathematics
at the Hebrew University of Jerusalem
and Rutgers University
in New Jersey
.
. He received his Ph.D.
in 1969 from the Hebrew University.
Shelah is married to Yael, and has three children.
, model theory
in particular, and in axiomatic set theory.
In model theory
, he developed the classification theory, which led him to a solution of Morley's problem. In set theory
, he invented 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 Kurosh monster, 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.
Israel
The State of Israel is a parliamentary republic located in the Middle East, along the eastern shore of the Mediterranean Sea...
i mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. He is a professor of mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
at the Hebrew University of Jerusalem
Hebrew University of Jerusalem
The Hebrew University of Jerusalem ; ; abbreviated HUJI) is Israel's second-oldest university, after the Technion – Israel Institute of Technology. The Hebrew University has three campuses in Jerusalem and one in Rehovot. The world's largest Jewish studies library is located on its Edmond J...
and Rutgers University
Rutgers University
Rutgers, The State University of New Jersey , is the largest institution for higher education in New Jersey, United States. It was originally chartered as Queen's College in 1766. It is the eighth-oldest college in the United States and one of the nine Colonial colleges founded before the American...
in New Jersey
New Jersey
New Jersey is a state in the Northeastern and Middle Atlantic regions of the United States. , its population was 8,791,894. It is bordered on the north and east by the state of New York, on the southeast and south by the Atlantic Ocean, on the west by Pennsylvania and on the southwest by Delaware...
.
Biography
Shelah was born in Jerusalem on July 3, 1945. He is the son of the Israeli poet and political activist Yonatan RatoshYonatan Ratosh
Uriel Shelach , better known by his pen name Yonatan Ratosh , was an Israeli poet and the founder of the Canaanite movement.-Biography :...
. He received his Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
in 1969 from the Hebrew University.
Shelah is married to Yael, and has three children.
Academic career
Shelah is one of the most prolific contemporary mathematicians. As of 2009, he has published nearly 900 mathematical papers (together with over 200 co-authors). His main interests lie in mathematical logicMathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
, model theory
Model theory
In mathematics, model theory is the study of mathematical structures using tools from mathematical logic....
in particular, and in axiomatic set theory.
In model theory
Model theory
In mathematics, model theory is the study of mathematical structures using tools from mathematical logic....
, he developed the classification theory, which led him to a solution of Morley's problem. In set theory
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
, he invented the notion of proper forcing
Proper Forcing Axiom
In the mathematical field of set theory, the proper forcing axiom is a significant strengthening of Martin's axiom, where forcings with the countable chain condition are replaced by proper forcings.- Statement :...
, an important tool in iterated forcing
Forcing (mathematics)
In the mathematical discipline of set theory, forcing is a technique invented by Paul Cohen for proving consistency and independence results. It was first used, in 1963, to prove the independence of the axiom of choice and the continuum hypothesis from Zermelo–Fraenkel set theory...
arguments. With PCF theory
PCF theory
PCF theory is the name of a mathematical theory, introduced by Saharon , that deals with the cofinality of the ultraproducts of ordered sets. It gives strong upper bounds on the cardinalities of power sets of singular cardinals, and has many more applications as well...
, he showed that in spite of the undecidability of the most basic questions of cardinal arithmetic (such as the continuum hypothesis
Continuum hypothesis
In mathematics, the continuum hypothesis is a hypothesis, advanced by Georg Cantor in 1874, about the possible sizes of infinite sets. It states:Establishing the truth or falsehood of the continuum hypothesis is the first of Hilbert's 23 problems presented in the year 1900...
), there are still highly nontrivial ZFC
Zermelo–Fraenkel set theory
In mathematics, Zermelo–Fraenkel set theory with the axiom of choice, named after mathematicians Ernst Zermelo and Abraham Fraenkel and commonly abbreviated ZFC, is one of several axiomatic systems that were proposed in the early twentieth century to formulate a theory of sets without the paradoxes...
theorems about cardinal
Cardinal number
In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality of sets. The cardinality of a finite set is a natural number – the number of elements in the set. The transfinite cardinal numbers describe the sizes of infinite...
exponentiation. Shelah constructed a Kurosh monster, 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
Arrow's impossibility theorem
In social choice theory, Arrow’s impossibility theorem, the General Possibility Theorem, or Arrow’s paradox, states that, when voters have three or more distinct alternatives , no voting system can convert the ranked preferences of individuals into a community-wide ranking while also meeting a...
on voting systems.
Awards
- The first recipient of the Erdős PrizeErdős Prize- References :*...
, in 1977; - The Israel PrizeIsrael PrizeThe Israel Prize is an award handed out by the State of Israel and is largely regarded as the state's highest honor. It is presented annually, on Israeli Independence Day, in a state ceremony in Jerusalem, in the presence of the President, the Prime Minister, the Knesset chairperson, and the...
, for mathematics, in 1998; - The Bolyai PrizeBolyai PrizeThe International Bolyai János Prize of Mathematics is an international prize for mathematicians founded by the Hungarian Academy of Sciences. The prize is awarded in every five years to mathematicians having published their monograph describing their own highly important new results in the past 10...
in 2000; - The Wolf Prize in MathematicsWolf Prize in MathematicsThe Wolf Prize in Mathematics is awarded almost annually by the Wolf Foundation in Israel. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Medicine, Physics and Arts...
in 2001. - The EMET prize in 2011.
External links
- Archive of Shelah's mathematical papers, shelah.logic.at
- A survey of recent work on AECs, math.uic.edu
See also
- List of Israel Prize recipients