**Saharon Shelah** is an Israeli mathematician who worked in America on mathematical logic.

- Shelah attended Tel Aviv University and was awarded his B.Sc. in 1964.
- Shelah was awarded a Ph.D. in 1969 for his work on stable theories.
- After completing his doctorate, Shelah spent the year 1969-70 as a Lecturer at Princeton University and the following year 1970-71 as an Assistant Professor at the University of California, Los Angeles.
- We look at Shelah's mathematical contributions by first recording the awards that he has received and we quote from the citations of these.
- In 1977, Shelah was awarded the Anna and Lajos Erdős Prize in Mathematics.
- Shelah was only 32 years old when he received the prize.
- The Bolyai Prize Committee decided to award the 2000 Bolyai prize to Shelah for his monograph Cardinal arithmetic (1994).
- The one other modern mathematician who sustained a comparable level of productivity on paper was Paul Erdős, and in an interview that appeared in 1985 he singled out Shelah among all mathematicians for praise.
- This theory, created by Shelah, became a major branch of set-theoretic research since the late 1980's, illuminating many issues involving singular cardinals in combinatorial set theory and the theory of large cardinals.
- One of the features of the theory, emphasized by Shelah himself as well, is that it has led to a plethora of direct theorems of set theory, as opposed to relative consistency results.
- The proof of such a result was considered inconceivable to any expert before Shelah.
- Shelah created a number of subfields of set theory, most notably the theory of proper forcing and the theory of possible cofinalities, which is a remarkable refinement of the notion of cardinality and which led to proofs of definite statements in areas previously considered far beyond the limits of undecidability.
- In the course of examining the awards made to Shelah we have given details of his famous book Cardinal Arithmetic (1994).
- In 1982 Shelah published his now classic text Proper forcing.
- Shelah came to proper forcing in the late 1970's, and in a timely tract (the first edition of the present text) communicated the subject to an excited set theory community.
- The tract in fact went far beyond its title to bring together much of Shelah's work in set theory to that time, and the wealth of information and techniques therein greatly stimulated set-theoretic research in the ensuing years.
- Time passed, and with Shelah's inimitable English and expositional gaps having become legion and a steady stream of new results having been established, it became apparent that a mature, magisterial presentation of proper forcing in all of its aspects was needed.
- In set theory Shelah is initially stimulated by specific problems.
- A telling point is that when some local flaw is pointed out to Shelah, he is usually able to come up quickly with another idea for crossing that bridge.
- Shelah's written accounts have acquired a certain notoriety that in large part has to do with his insistence that his edifices be regarded as autonomous mental constructions.
- Shelah regards the written word as necessary and central for capturing and fixing a construction, and so for him getting everything down on paper is of crucial importance.
- In mathematics one often aspires to the most elegant or definitive treatment; in contrast, Shelah's work features a continuing, dynamic self-dialogue, one that pushes to the limits of exposition.
- While there is a particular drive to solve specific problems, Shelah with his generalizing approach is able to draw out larger, recurring patterns that lead to new techniques that soon get elevated to methods.
- Shelah started out in model theory, developing an abstract classification theory for models which is a continuing research program for him and model theorists to this day.
- In the mid-1970's, in his first major body of results in set theory, Shelah resolved a long-standing problem in abelian group theory, Whitehead's problem, by establishing both the consistency and the independence of the corresponding proposition.
- It is through these beginnings, motivated by the set-theoretic problems that arose, that Shelah started to develop a general theory of iterated forcing for the continuum.
- In November 2009, MathSciNet listed the truly remarkable number of 867 publications for Shelah.

Born 3 July 1945, Jerusalem, British Mandate for Palestine (now Israel).

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Origin Israel, Prize Wolf

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive