Saharon Shelah (שהרן שלח, born July 3, 1945 in Jerusalem) is an Israeli mathematician. He is a professor of mathematics at the Hebrew University of Jerusalem and also at Rutgers University in New Jersey, USA. Shelah's main interest lies in mathematical logic, in particular in model theory and set theory. Image File history File linksMetadata Size of this preview: 450 × 600 pixelsFull resolution (1200 × 1600 pixel, file size: 846 KB, MIME type: image/jpeg) File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): Saharon Shelah Metadata This file contains... “Rutgers” redirects here. ... September 6 is the 249th day of the year (250th in leap years). ... 2005 (MMV) was a common year starting on Saturday of the Gregorian calendar. ... July 3 is the 184th day of the year (185th in leap years) in the Gregorian calendar, with 181 days remaining. ... 1945 (MCMXLV) was a common year starting on Monday. ... For other uses, see Jerusalem (disambiguation). ... For other uses, see Jerusalem (disambiguation). ... The word Jew ( Hebrew: יהודי) is used in a wide number of ways, but generally refers to a follower of the Jewish faith, a child of a Jewish mother, or someone of Jewish descent with a connection to Jewish culture or ethnicity and often a combination... Leonhard Euler is considered by many to be one of the greatest mathematicians of all time A mathematician is the person whose primary area of study and research is the field of mathematics. ... The Hebrew University of Jerusalem (האוניברסיטה העברית בירושלים) is one of Israels biggest and most important institutes of higher learning and research. ... “Rutgers” redirects here. ... The Hebrew University of Jerusalem (האוניברסיטה העברית בירושלים) is one of Israels biggest and most important institutes of higher learning and research. ... Michael Oser Rabin (born 1931 in Breslau, Germany, today in Poland) is a noted computer scientist and a recipient of the Turing Award, the most prestigious award in the field. ... Rami Grossberg is an associate professor of mathematics at Carnegie Mellon University and a leading researcher in model theory. ... Mathematical logic is a subfield of mathematics that is concerned with formal systems in relation to the way that they encode intuitive concepts of mathematical objects such as sets and numbers, proofs, and computation. ... In mathematics, model theory is the study of the representation of mathematical concepts in terms of set theory, or the study of the structures that underlie mathematical systems. ... This article or section is in need of attention from an expert on the subject. ... The Wolf Prize has been awarded annually since 1978 to living scientists and artists for achievements in the interest of mankind and friendly relations among peoples . ... The Israel Prize is the most prestigious award handed out by the State of Israel. ... Yonatan Ratosh, Israeli poet, was born in 1908 in Russia, but his dedicated Zionist parents educated his siblings and him to speak, read and write only in Hebrew. ... July 3 is the 184th day of the year (185th in leap years) in the Gregorian calendar, with 181 days remaining. ... 1945 (MCMXLV) was a common year starting on Monday. ... For other uses, see Jerusalem (disambiguation). ... Leonhard Euler is considered by many to be one of the greatest mathematicians of all time A mathematician is the person whose primary area of study and research is the field of mathematics. ... Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... The Hebrew University of Jerusalem (האוניברסיטה העברית בירושלים) is one of Israels biggest and most important institutes of higher learning and research. ... “Rutgers” redirects here. ... It has been suggested that this article be split into multiple articles. ... Mathematical logic is a subfield of mathematics that is concerned with formal systems in relation to the way that they encode intuitive concepts of mathematical objects such as sets and numbers, proofs, and computation. ... In mathematics, model theory is the study of the representation of mathematical concepts in terms of set theory, or the study of the structures that underlie mathematical systems. ... This article or section is in need of attention from an expert on the subject. ...

Shelah is one of the most prolific contemporary mathematicians. As of 2006, he had (together with over 200 coauthors) published nearly 900 mathematical papers. Among his most important results are: For the Manfred Mann album, see 2006 (album). ...

• in model theory, the introduction and development of his classification theory, which led him to a solution of Morley's problem
• in set theory,
  • the invention of the notion of proper forcing, an important tool in iterated forcing arguments
  • PCF theory, which shows that in spite of the undecidability of the most basic questions of cardinal arithmetic (such as the continuum hypothesis), there are highly nontrivial ZFC theorems about cardinal exponentiation, after all.

Shelah also solved several outstanding questions from other fields, among them: In mathematics, model theory is the study of the representation of mathematical concepts in terms of set theory, or the study of the structures that underlie mathematical systems. ... Is this referring to IX, 1. ... Set theory is the mathematical theory of sets, which represent collections of abstract objects. ... In axiomatic set theory, forcing is a technique, invented by Paul Cohen, for proving consistency and independence results with respect to the Zermelo-Fraenkel axioms. ... PCF theory is the name of a mathematical theory, invented by Saharon Shelah, that deals with power sets of singular cardinals. ... In mathematics, the continuum hypothesis is a hypothesis about the possible sizes of infinite sets. ... Zermelo–Fraenkel set theory, with the axiom of choice, commonly abbreviated ZFC, is the most common form of axiomatic set theory, and as such is the most common foundation of mathematics. ... Aleph-0, the smallest infinite cardinal In mathematics, cardinal numbers, or cardinals for short, are a generalized kind of number used to denote the size of a set. ...

• 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).
• He extended Arrow's impossibility theorem on voting systems.

Shelah is the son of the Israeli poet and political activist Yonatan Ratosh.^[1] He is married to Yael,^[1] and has three children.^[2] In group theory, the Whitehead problem is the following question: Is every abelian group A with Ext1(A, Z) = 0 a free abelian group? The condition Ext1(A, Z) = 0 can be equivalently formulated as follows: whenever B is an abelian group and f : B → A is a surjective group... In computability theory, primitive recursive functions are a class of functions which form an important building block on the way to a full formalization of computability. ... Van der Waerdens theorem is a theorem of the branch of mathematics called Ramsey theory. ... In voting systems, Arrow’s impossibility theorem, or Arrow’s paradox, demonstrates that no voting system can possibly meet a certain set of reasonable criteria when there are three or more options to choose from. ... Yonatan Ratosh, Israeli poet, was born in 1908 in Russia, but his dedicated Zionist parents educated his siblings and him to speak, read and write only in Hebrew. ...

References

1. ^ ^{a b} Shelah, Saharon (April 5, 2001). זיכרונותיו של בן (Memoirs of a Son) ((Hebrew)). Haaretz. Retrieved on 2007-03-14. “כשעמדתי להציג לפני חברתי יעל (עתה רעייתי) את בני משפחתי…הפרופ' שהרן שלח מן האוניברסיטה העברית בירושלים, בנו של יונתן רטוש…”
2. ^ Réka, Szász (March 2001). Harc a matematikával és a titkárnőkkel ((Hungarian)). Magyar Tudományos. Retrieved on 2007-03-16. “Hungarian: A gyerekei mivel foglalkoznak? A nagyobbik fiam zeneelméletet tanul, a lányom történelmet, a kisebbik fiam pedig biológiát. What are your children doing? My oldest son is learning the theory of music, my daughter history, my youngest son biology.”

April 5 is the 95th day of the year in the Gregorian calendar (96th in leap years). ... 2001 (MMI) was a common year starting on Monday of the Gregorian calendar. ... Haaretz (Hebrew: (help· info), The Land) is an Israeli newspaper, founded in 1919. ... 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the Anno Domini era. ... For the Lebanese political coalition, see March 14 Alliance. ... 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the Anno Domini era. ... March 16 is the 75th day of the year in the Gregorian calendar (76th in leap years). ...

External links

• Saharon Shelah at the Mathematics Genealogy Project
• Archive of Shelah's mathematical papers