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Saharon Shelah

 
Saharon Shelah

 
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Saharon Shelah
 
 
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Saharon Shelah (born July 3, 1945 in Jerusalem
Jerusalem

Jerusalem is the capital of Israel and its List of Israeli cities in both population and area, with a population of 747,600 residents over an area of if Positions on Jerusalem East Jerusalem is included....
) is an Israel
Israel

Israel officially the State of Israel , is a country in the Middle East 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 relatively small area....
i mathematician
Mathematician

A mathematician is a person whose primary area of study and/or research is the field of mathematics....
. He is a professor of mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
 at the Hebrew University of Jerusalem
Hebrew University of Jerusalem

The Hebrew University of Jerusalem is Israel's oldest university.The First Board of Governors included Albert Einstein, Sigmund Freud, Martin Buber, and Chaim Weizmann....
 and also at Rutgers University
Rutgers University

Rutgers, The State University of New Jersey , is the largest institution for higher education in the U.S. state of New Jersey. It was originally chartered as Queen's College in 1766 and is the Colonial colleges in the United States....
 in New Jersey
New Jersey

New Jersey is a state in the Mid-Atlantic States and Northeastern United States regions of the United States. It is bordered on the north by New York, on the east by the Hudson River and the Atlantic Ocean, on the southwest by Delaware, and on the west by Pennsylvania....
, U.S.
United States

The United States of America is a Federal government constitutional republic comprising U.S. state and a federal district. The country is situated mostly in central North America, where its Contiguous United States and Washington, D.C., the Capital districts and territories, lie between the Pacific Ocean and Atlantic Oceans, Borders of the U...
. Shelah's main interest lies in mathematical logic
Mathematical logic

Mathematical logic is a subfield of mathematics and logic with close connections to computer science and philosophical logic. The field includes the mathematical study of logic and the applications of formal logic to other areas of mathematics....
, in particular in model theory
Model theory

In mathematics, model theory is the study of mathematical Structure such as Group , fields, graph , or even models of set theory, using tools from mathematical logic....
 and set theory.

He received his Ph.D.
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...
 in 1969 from the Hebrew University.

Shelah is one of the most prolific contemporary mathematicians. As of 2006, he had (together with over 200 co-authors) published nearly 900 mathematical papers.






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Saharon Shelah (born July 3, 1945 in Jerusalem
Jerusalem

Jerusalem is the capital of Israel and its List of Israeli cities in both population and area, with a population of 747,600 residents over an area of if Positions on Jerusalem East Jerusalem is included....
) is an Israel
Israel

Israel officially the State of Israel , is a country in the Middle East 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 relatively small area....
i mathematician
Mathematician

A mathematician is a person whose primary area of study and/or research is the field of mathematics....
. He is a professor of mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
 at the Hebrew University of Jerusalem
Hebrew University of Jerusalem

The Hebrew University of Jerusalem is Israel's oldest university.The First Board of Governors included Albert Einstein, Sigmund Freud, Martin Buber, and Chaim Weizmann....
 and also at Rutgers University
Rutgers University

Rutgers, The State University of New Jersey , is the largest institution for higher education in the U.S. state of New Jersey. It was originally chartered as Queen's College in 1766 and is the Colonial colleges in the United States....
 in New Jersey
New Jersey

New Jersey is a state in the Mid-Atlantic States and Northeastern United States regions of the United States. It is bordered on the north by New York, on the east by the Hudson River and the Atlantic Ocean, on the southwest by Delaware, and on the west by Pennsylvania....
, U.S.
United States

The United States of America is a Federal government constitutional republic comprising U.S. state and a federal district. The country is situated mostly in central North America, where its Contiguous United States and Washington, D.C., the Capital districts and territories, lie between the Pacific Ocean and Atlantic Oceans, Borders of the U...
. Shelah's main interest lies in mathematical logic
Mathematical logic

Mathematical logic is a subfield of mathematics and logic with close connections to computer science and philosophical logic. The field includes the mathematical study of logic and the applications of formal logic to other areas of mathematics....
, in particular in model theory
Model theory

In mathematics, model theory is the study of mathematical Structure such as Group , fields, graph , or even models of set theory, using tools from mathematical logic....
 and set theory.

He received his Ph.D.
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...
 in 1969 from the Hebrew University.

Shelah is one of the most prolific contemporary mathematicians. As of 2006, he had (together with over 200 co-authors) published nearly 900 mathematical papers. Among his most important results are:

  • in model theory
    Model theory

    In mathematics, model theory is the study of mathematical Structure such as Group , fields, graph , or even models of set theory, using tools from mathematical logic....
    , the introduction and development of his 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 Set , 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....
    ,
    • the invention of the notion of proper forcing, 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 1962, to prove the independence of the continuum hypothesis and the axiom of choice from Zermelo-Fraenkel set theory....
       arguments
    • PCF theory
      PCF theory

      PCF theory is the name of a mathematics theory, invented by Saharon Shelah, that deals with the cofinality of the ultraproducts of ordered sets....
      , which shows 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, about the possible sizes of infinite Set . Cantor introduced the concept of cardinal number to compare the sizes of infinite sets, and he gave two proofs that the cardinality of the set of integers is strictly smaller than that of the set of real numbers....
      ), there are highly nontrivial ZFC
      Zermelo–Fraenkel set theory

      Zermelo?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 foundations of mathematics....
       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 Set ....
       exponentiation, after all.


Shelah also solved several outstanding questions from other fields, among them:
  • He 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)
    Van der Waerden's theorem

    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....
    .
  • He extended Arrow's impossibility theorem
    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 reasonable criteria with three or more discrete options to choose from....
     on voting systems.


Shelah was awarded the Bolyai prize
Bolyai Prize

The International Bolyai J?nos 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 years....
 in 2000.

Shelah is the son of the Israeli poet and political activist Yonatan Ratosh
Yonatan Ratosh

Yonatan Ratosh , was the Pen name of Israeli poet Uriel Shelach ....
. He is married to Yael, and has three children.

External links