Azriel Levy

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

life and work

Levy received his PhD in 1958 from the Hebrew University of Jerusalem under Abraham Fraenkel and Abraham Robinson (Contributions to the Metamathematics of Set Theory) . In 1958/1958 he was a post-doctoral student and Sloan Fellow at the Massachusetts Institute of Technology . 1959 to 1961 he was an assistant professor at the University of California, Berkeley . From 1961 he was at the Hebrew University, where he became professor of mathematics and has been professor emeritus since 2003 . He was visiting professor at Yale University and the University of California, Los Angeles, among others .

Levy made fundamental contributions to axiomatic set theory. From him come a theory of relative constructibility , the Levy hierarchy and the concept of the Levy collapse of cardinal numbers. He was one of the first to use Cohen's forcing method , along with Solomon Feferman, after its introduction in the early 1960s. For example, he proved with James Halpern in 1971 that the ultrafilter lemma as an axiom does not result in the axiom of choice . Conversely, since it follows from the axiom of choice and is independent of the Zermelo-Fraenkel set theory , it is a weaker axiom than the axiom of choice, but not redundant to ZF.

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

With Robert Solovay he showed that measurable cardinal numbers retain their properties even with mild forcing extensions. These results contributed to the conviction that the simple addition of axioms of large cardinal numbers to the Zermelo-Fraenkel set theory could not decide the continuum hypothesis.

In 1962 he gave a lecture at the International Congress of Mathematicians in Stockholm ( The interdependence of some consequences of the axiom of choice ).

His PhD students include Menachem Magidor , Moti Gitik and Dov Gabbay .

Fonts

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

literature

• Akihiro Kanamori: Levy and Set Theory. In: Annals of Pure and Applied Logic. 2006. (PDF file; 1.64 MB)

Web links

• Literature by and about Azriel Levy in the catalog of the German National Library
• AZRIEL LEVY, PROFESSOR OF MATHEMATICS . Entry on the website of the Hebrew University of Jerusalem.

Individual evidence

1. ^ JD Halpern, A. Levy: The Boolean prime ideal theorem does not imply the axiom of choice, Axiomatic Set Theory. Symposia Pure Math. 1971, pp. 83-134.
2. ^ Azriel Levy, Robert Solovay: Measurable cardinals and the Continuum Hypothesis. In: Israel J. Mathematics. Volume 5, 1967, pp. 235-248.