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.
Shelah is one of the most prolific contemporary mathematicians. As of 2003, he has (together with about 190 coauthors) published more than 750 mathematical papers. Among his most important results are:
- 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:
- He constructed a Kurosh monster, a group of cardinality with no proper subgroup of the same cardinality.
- He showed that Whitehead's problem is independent from 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.