Azriel Lévy (; born c. 1934) is an Israeli

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

, logician, and a

professor emeritus ''Emeritus/Emerita'' () is an honorary title granted to someone who retirement, retires from a position of distinction, most commonly an academic faculty position, but is allowed to continue using the previous title, as in "professor emeritus". ...

at the

Hebrew University of Jerusalem The Hebrew University of Jerusalem (HUJI; ) is an Israeli public university, public research university based in Jerusalem. Co-founded by Albert Einstein and Chaim Weizmann in July 1918, the public university officially opened on 1 April 1925. ...

Biography

Lévy obtained his Ph.D. at the

in 1958, under the supervision of

Abraham Fraenkel Abraham Fraenkel (; 17 February, 1891 – 15 October, 1965) was a German-born Israeli mathematician. He was an early Zionist and the first Dean of Mathematics at the Hebrew University of Jerusalem. He is known for his contributions to axiomatic ...

and Abraham Robinson. Later, using Cohen's method of forcing, he proved several results on the

consistency In deductive logic, a consistent theory is one that does not lead to a logical contradiction. A theory T is consistent if there is no formula \varphi such that both \varphi and its negation \lnot\varphi are elements of the set of consequences ...

of various statements contradicting the

axiom of choice In mathematics, the axiom of choice, abbreviated AC or AoC, is an axiom of set theory. Informally put, the axiom of choice says that given any collection of non-empty sets, it is possible to construct a new set by choosing one element from e ...

. For example, with J. D. Halpern he proved that the

Boolean prime ideal theorem In mathematics, the Boolean prime ideal theorem states that Ideal (order theory), ideals in a Boolean algebra (structure), Boolean algebra can be extended to Ideal (order theory)#Prime ideals , prime ideals. A variation of this statement for Filte ...

does not imply the axiom of choice. He discovered the models ''L'' 'x''used in

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 extensi ...

. He also introduced the notions of Lévy hierarchy of the formulas of

set theory Set theory is the branch of mathematical logic that studies Set (mathematics), sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathema ...

, Levy collapse and the Feferman–Levy model. His students include Dov Gabbay, Moti Gitik, and Menachem Magidor.

Selected works

* * A. Lévy: ''A hierarchy of formulas in set theory'', Memoirs of the American Mathematical Society, 57, 1965. * J. D. Halpern, A. Lévy: The Boolean prime ideal theorem does not imply the axiom of choice,

Axiomatic Set Theory Set theory is the branch of mathematical logic that studies Set (mathematics), sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathema ...

, Symposia Pure Math., 1971, 83–134. * A. Lévy: ''Basic Set Theory'', Springer-Verlag, Berlin, 1979, 391 pages; reprinted by Dover Publications, 2003.

Notes

References

External links

* 1934 births Living people Israeli mathematicians Set theorists Academic staff of the Hebrew University of Jerusalem Hebrew University of Jerusalem alumni {{asia-mathematician-stub