Azriel Levy is an Israeli mathematician, logician, and a professor emeritus at the Hebrew University of Jerusalem

Hebrew University of Jerusalem

The Hebrew University of Jerusalem ; ; abbreviated HUJI) is Israel's second-oldest university, after the Technion – Israel Institute of Technology. The Hebrew University has three campuses in Jerusalem and one in Rehovot. The world's largest Jewish studies library is located on its Edmond J...

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He obtained his Ph.D. at the Hebrew University of Jerusalem

Hebrew University of Jerusalem

The Hebrew University of Jerusalem ; ; abbreviated HUJI) is Israel's second-oldest university, after the Technion – Israel Institute of Technology. The Hebrew University has three campuses in Jerusalem and one in Rehovot. The world's largest Jewish studies library is located on its Edmond J...

 in 1958, under the supervision of Abraham Fraenkel and Abraham Robinson

Abraham Robinson

Abraham Robinson was a mathematician who is most widely known for development of non-standard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were incorporated into mathematics....

. Using Cohen

Paul Cohen (mathematician)

Paul Joseph Cohen was an American mathematician best known for his proof of the independence of the continuum hypothesis and the axiom of choice from Zermelo–Fraenkel set theory, the most widely accepted axiomatization of set theory.-Early years:Cohen was born in Long Branch, New Jersey, into a...

's method of 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 1963, to prove the independence of the axiom of choice and the continuum hypothesis from Zermelo–Fraenkel set theory...

, he proved several results on the consistency of various statements contradicting the axiom of choice. For example, with J. D. Halpern he proved that the Boolean prime ideal theorem

Boolean prime ideal theorem

In mathematics, a prime ideal theorem guarantees the existence of certain types of subsets in a given abstract algebra. A common example is the Boolean prime ideal theorem, which states that ideals in a Boolean algebra can be extended to prime ideals. A variation of this statement for filters on...

 does not imply the axiom of choice. He discovered the models L[x] used in inner model theory

Inner model theory

In set theory, inner model theory is the study of certain models of ZFC or some fragment or strengthening thereof. Ordinarily these models are transitive subsets or subclasses of the von Neumann universe V, or sometimes of a generic extension of V. Inner model theory studies the relationships of...

. He also introduced the notions of Levy hierarchy of the formulas of set theory and Levy collapse.
His notable students include Dov Gabbay

Dov Gabbay

Dov M. Gabbay is Augustus De Morgan Professor of Logic at the Group of Logic, Language and Computation, Department of Computer Science, King's College London . He has authored over four hundred and fifty research papers and over thirty research monographs...

, Moti Gitik

Moti Gitik

Moti Gitik is a mathematician, working in set theory. Gitik is professor at the Tel-Aviv University. He proved the consistency of "all uncountable cardinals are singular" from the consistency of "there is a proper class of strongly compact cardinals"...

, Menachem Magidor

Menachem Magidor

Menachem Magidor is an Israeli mathematician who specializes in mathematical logic, in particular set theory. He served as President of the Hebrew University of Jerusalem.- Biography :Menachem Magidor was born in Petah Tikva on January 24, 1946....

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Selected works

• A. Levy: A hierarchy of formulas in set theory, Memoirs of the American Mathematical Society, 57, 1965.
• J. D. Halpern, A. Levy: The Boolean prime ideal theorem does not imply the axiom of choice, Axiomatic Set Theory, Symposia Pure Math., 1971, 83–134.
• A. Levy: Basic Set Theory, Springer-Verlag, Berlin, 1979, 391 pages. Reprinted by Dover Publications, 2003.

External links