Saharon Shelah ' onMouseout='HidePop("38060")' href="http://www.absoluteastronomy.com/topics/Jerusalem">Jerusalem
Jerusalem is the capital of Israel and its largest city in both population and area, with a population of 747,600 residents over an area of if disputed East Jerusalem is included...
) is an
IsraelIsrael officially the State of Israel , is a developed state in Western Asia located on the eastern shore of the Mediterranean Sea. It borders Lebanon in the north, Syria in the northeast, Jordan in the east, and Egypt on the southwest, and contains geographically diverse features within its...
i
mathematicianA mathematician is a person whose primary area of study and/or research is the field of mathematics. Mathematicians are concerned with particular problems related to logic, space, transformations, numbers and more general ideas which encompass these concepts...
.
Life
Shelah received his
Ph.D.Ph.D. or PHD may stand for:* Doctor of Philosophy, an academic degree* Ph.D. , a 1980s British group* Piled Higher and Deeper, a web comic strip* PhD: Phantasy Degree, a Korean comic series* Parisada Hindu Dharma, an Indonesian organization...
in 1969 from the Hebrew University. He is a professor of
mathematicsMathematics is the science and study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions....
at the
Hebrew University of JerusalemThe Hebrew University of Jerusalem is Israel's oldest university....
and also at
Rutgers UniversityRutgers, The State University of New Jersey , is the largest institution for higher education in the state of New Jersey. It was originally chartered as Queen's College in 1766 and is the eighth-oldest college in the United States...
in
New JerseyNew Jersey is a state in the Mid-Atlantic region of the United States. It is bordered on the north by New York, and to the east by the Hudson River, Upper New York Bay, the Kill Van Kull, Newark Bay, the Arthur Kill, Raritan Bay, Sandy Hook Bay, Westchester County, New York City, Long Island, and...
,
U.S.The United States of America is a federal constitutional republic comprising fifty states and a federal district...
.
Shelah is the son of the Israeli poet and political activist
Yonatan RatoshYonatan Ratosh , was the pen name of Israeli poet Uriel Shelach .-Biography:Born Uriel Heilperin in the Russian Empire in 1908 to a Zionist family. His father, Yechiel, was a Hebraist educator and raised Ratosh and his siblings in Hebrew...
.
He is married to Yael, and has three children.
Accomplishments
Shelah is one of the most prolific contemporary mathematicians. As of 2009, he has (together with over 200 co-authors) published nearly 900 mathematical papers. His main interests lie in
mathematical logicMathematical logic is a subfield of mathematics with close connections to 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 theoryIn mathematics, model theory is the study of mathematical structures such as groups, fields, graphs, or even universes of set theory, using tools from mathematical logic. A structure that gives meaning to the sentences of a formal language is called a model for the language...
in particular, and in axiomatic set theory.
Among his important results are:
- In model theory
In mathematics, model theory is the study of mathematical structures such as groups, fields, graphs, or even universes of set theory, using tools from mathematical logic. A structure that gives meaning to the sentences of a formal language is called a model for the language...
, the introduction and development of his classification theory, which led him to a solution of Morley's problem
- In set theory
The modern study of set theory was initiated by Cantor and Dedekind in the 1870s. After the discovery of paradoxes in informal set theory, numerous axiom systems were proposed in the early twentieth century, of which the Zermelo–Fraenkel axioms, with the axiom of choice, are the best-known.The...
:
- The invention of the notion of proper forcing, an important tool in iterated forcing
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 1962, to prove the independence of the continuum hypothesis and the axiom of choice from Zermelo–Fraenkel set theory...
arguments;
- PCF theory
PCF theory is the name of a mathematical theory, invented by Saharon Shelah, 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...
, which shows that in spite of the undecidability of the most basic questions of cardinal arithmetic (such as the continuum hypothesisIn mathematics, the continuum hypothesis is a hypothesis, advanced by Georg Cantor in 1877, about the possible sizes of infinite sets. It states:Establishing the truth or falsehood of the continuum hypothesis is the first of Hilbert's twenty-three problems presented in the year 1900...
), there are highly nontrivial ZFCZermelo–Fraenkel set theory with the axiom of choice, commonly abbreviated ZFC, is the standard form of axiomatic set theory and as such is the most common foundation of mathematics...
theorems about cardinalIn 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, after all.
Shelah has also made major contributions to other fields. For example, he:
- Constructed a Kurosh monster, an uncountable group for which every proper subgroup is countable;
- Showed that Whitehead's problem is independent of ZFC;
- Gave the first primitive recursive upper bound to van der Waerden's numbers V(C,N)
Van der Waerden's theorem is a theorem in the branch of mathematics called Ramsey theory. The theorem is about the basic structure of the integers. It is named after the Dutch mathematician B. L...
;
- Extended Arrow's impossibility theorem
In social choice theory, Arrow’s impossibility theorem, or Arrow’s paradox, demonstrates that no voting system can convert the ranked preferences of individuals into a community-wide ranking while also meeting a certain set of criteria with three or more discrete options to choose from...
on voting systems.
Shelah has been awarded the following prizes:
- The first Erdős Prize
The Anna and Lajos Erdős Prize in Mathematics is a prize given by the Israel Mathematical Union to an Israeli mathematician , "with preference to candidates up to the age of 40." The prize was established by Paul Erdős in 1977 in honor of his parents, and is awarded annually or biannually...
in 1977;
- The Israel Prize
The 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 prize
The 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 Mathematics
The Wolf Prize in Mathematics is awarded almost annually by the Wolf Foundation. 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.
External links
See also
- List of Israel Prize recipients