Saharon Shelah

Saharon Shelah (; , ; born July 3, 1945) is an Israeli mathematician. He is a professor of mathematics at the Hebrew University of Jerusalem and Rutgers University in New Jersey.

Biography Shelah was born in Jerusalem on July 3, 1945. He is the son of the Hebrew poet and Canaanist political activist Yonatan Ratosh. He attended Tichon Hadash high school in Tel Aviv. He received his PhD for his work on stable theories in 1969 from the Hebrew University.

Shelah is married to Yael, His brother, magistrate judge Hamman Shelah was murdered along with his wife and daughter by an Egyptian soldier in the Ras Burqa massacre in 1985.

Shelah planned to be a scientist while at primary school, but initially was attracted to physics and biology, not mathematics. Later he found mathematical beauty in studying geometry: He said, "But when I reached the ninth grade I began studying geometry and my eyes opened to that beauty—a system of demonstration and theorems based on a very small number of axioms which impressed me and captivated me." At the age of 15, he decided to become a mathematician, a choice cemented after reading Abraham Halevy Fraenkel's book An Introduction to Mathematics. He then worked as a teaching assistant at the Institute of Mathematics of the Hebrew University of Jerusalem while completing a Ph.D. there under the supervision of Michael Oser Rabin, He is a prolific author, with more than 1100 peer-reviewed research papers since his first in 1969.

In model theory, he developed classification theory, which led him to a solution of Morley's problem. In set theory, he discovered the notion of proper forcing, an important tool in iterated forcing arguments. With PCF theory, he showed that in spite of the undecidability of the most basic questions of cardinal arithmetic (such as the continuum hypothesis), there are still highly nontrivial ZFC theorems about cardinal exponentiation. Shelah constructed a Jónsson group, 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.

Maryanthe Malliaris and Shelah studied Keisler's order, a construction from model theory, and in the process proved equality between two cardinal characteristics of the continuum, 𝖕 and 𝖙, resolving a problem that had been open for fifty years. This work earned them the 2017 Hausdorff Medal of the European Set Theory Society.

Shelah's work has had a deep impact on model theory and set theory. The tools he developed for his classification theory have been applied to a wide number of topics and problems in model theory and have led to great advances in stability theory and its uses in algebra and algebraic geometry as shown for example by Ehud Hrushovski and many others. Classification theory involves deep work developed in many dozens of papers to completely solve the spectrum problem on classification of first order theories in terms of structure and number of nonisomorphic models, a huge tour de force. Following that he has extended the work far beyond first order theories, for example for abstract elementary classes. This work also has had important applications to algebra by works of Boris Zilber.

Awards Three times speaker at the International Congress of Mathematicians (1974 invited, 1983 plenary, 1986 plenary) The first recipient of the Erdős Prize, in 1977 The Karp Prize of the Association for Symbolic Logic in 1983 The Israel Prize, for mathematics, in 1998 The Bolyai Prize in 2000 The Wolf Prize in Mathematics in 2001 The EMET Prize for Art, Science and Culture in 2011 The Leroy P. Steele Prize, for Seminal Contribution to Research, in 2013 Honorary member of the Hungarian Academy of Sciences, in 2013 Advanced grant of the European Research Council (2013) Hausdorff Medal of the European Set Theory Society, joint with Maryanthe Malliaris, 2017 Schock Prize in Logic and Philosophy of the Royal Swedish Academy of Sciences, 2018 Honorary doctorate from the Technische Universität Wien, 2019

Selected works Proper forcing, Springer 1982 Proper and improper forcing (2nd edition of Proper forcing), Springer 1998 Around classification theory of models, Springer 1986 Classification theory and the number of non-isomorphic models, Studies in Logic and the Foundations of Mathematics, 1978, 2nd edition 1990, Elsevier Classification Theory for Abstract Elementary Classes, College Publications 2009 Classification Theory for Abstract Elementary Classes, Volume 2, College Publications 2009 Cardinal Arithmetic, Oxford University Press 1994