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Azriel Levy (1934–) is an Israeli mathematician, logician, and a professor emeritus at the Hebrew University of Jerusalem
Hebrew University of Jerusalem

The Hebrew University of Jerusalem is Israel's oldest university.The First Board of Governors included Albert Einstein, Sigmund Freud, Martin Buber, and Chaim Weizmann....
.

He obtained his Ph.D. at the Hebrew University of Jerusalem in 1958, under the supervision of Fraenkel and 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 transfinite number numbers were incorporated into mathematics....
. Using Cohen
Paul Cohen (mathematician)

Paul Joseph Cohen was an United States 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....
'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 1962, to prove the independence of the continuum hypothesis and the axiom of choice from Zermelo-Fraenkel set theory....
, he proved several results on the consistency of various statements contradicting the axiom of choice
Axiom of choice

In mathematics, the axiom of choice, or AC, is an axiom of set theory. Informally put, the axiom of choice says that given any collection of bins, each containing at least one object, it is possible to make a selection of exactly one object from each bin, even if there are infinite set many bins and there is no "rule" for which object t...
. 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 ideal in a Boolean algebra can be extended to ideal ....
 does not imply the axiom of choice.






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Azriel Levy (1934–) is an Israeli mathematician, logician, and a professor emeritus at the Hebrew University of Jerusalem
Hebrew University of Jerusalem

The Hebrew University of Jerusalem is Israel's oldest university.The First Board of Governors included Albert Einstein, Sigmund Freud, Martin Buber, and Chaim Weizmann....
.

He obtained his Ph.D. at the Hebrew University of Jerusalem in 1958, under the supervision of Fraenkel and 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 transfinite number numbers were incorporated into mathematics....
. Using Cohen
Paul Cohen (mathematician)

Paul Joseph Cohen was an United States 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....
'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 1962, to prove the independence of the continuum hypothesis and the axiom of choice from Zermelo-Fraenkel set theory....
, he proved several results on the consistency of various statements contradicting the axiom of choice
Axiom of choice

In mathematics, the axiom of choice, or AC, is an axiom of set theory. Informally put, the axiom of choice says that given any collection of bins, each containing at least one object, it is possible to make a selection of exactly one object from each bin, even if there are infinite set many bins and there is no "rule" for which object t...
. 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 ideal in a Boolean algebra can be extended to ideal ....
 does not imply the axiom of choice. He also introduced the notions of Levy hierarchy of the formulas of set theory and Levy collapse
List of forcing notions

In mathematics, forcing is a method of constructing new models M[G] of set theory by adding a generic subset G of a poset P to a model M....
. 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....
, Moti Gitik, Menachem Magidor
Menachem Magidor

Menachem Magidor is an Israeli mathematician and a professor of mathematics at the Hebrew University of Jerusalem. His main research interest lies in mathematical logic, in particular in Axiomatic Set Theory....
.

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.


Reference

  • Akihiro Kanamori: , Annals of Pure and Applied Logic, 140(2006),233-252.


External links