Azriel Lévy

Azriel Levy (Hebrew עזריאל לוי, German transcription Azriel Levi, born in 1934 in Haifa) is an Israeli mathematical logician who particularly concerned with axiomatic set theory.

Life and work

Levy received his doctorate in 1958 at the Hebrew University of Jerusalem in Abraham Fraenkel and Abraham Robinson ( Contributions to the Metamathematics of Set Theory). 1958/1958 he was a post-doctoral researcher and Sloan Fellow at the Massachusetts Institute of Technology. 1959 to 1961 he was Assistant Professor at the University of California, Berkeley. From 1961 he was at the Hebrew University, where he became professor of mathematics and is since 2003 professor emeritus. He was a visiting professor at Yale University, among others, and the University of California, Los Angeles.

Levy made ​​fundamental contributions to axiomatic set theory. He wrote a theory of relative constructability, the Levy hierarchy and the concept of the Levy- collapse of cardinal numbers. He was one of the first who applied the early 1960s, in addition to Solomon Feferman Cohen's forcing method after their introduction. He showed, for example, with James Halpern 1971 that the Ultrafilterlemma as an axiom does not have the axiom of choice result. As it follows from the axiom of choice vice versa and is independent of the Zermelo -Fraenkel set theory, it is a weaker, Axiom as the axiom of choice, but not too ZF redundant.

He wrote a textbook on axiomatic set theory, after he had bought in 1973, the new edition of the classic textbook of his teacher Abraham Fraenkel and Yehoshua Bar - Hillel.

With Robert Solovay, he showed that measurable cardinals retain their properties even with mild forcing extensions. These results contributed to the conviction, which can not be decided by the simple addition of axioms of large cardinals for Zermelo -Fraenkel set theory, the continuum hypothesis.

In 1962 he was invited speaker at the International Congress of Mathematicians in Stockholm (The interdependence of some Consequences of the axiom of choice ).

His doctoral include Menachem Magidor, and Dov Gabbay Moti Gitik.

Writings

• A Hierarchy of formulas in set theory. In: Memoirs of the AMS. In 1965.
• Basic Set Theory. Springer 1979, Dover 2003.
• Mathematical Logic. Academon Press 1997. ( Hebrew)