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Fraenkel studied mathematics at the Universities of Munich, Berlin, Marburg and Breslau. After graduating, he lectured at the University of Marburg from 1916, and was promoted to professor in 1922.
In 1919 he married Wilhelmina Malka A. Prins (1892-1983). Due to the severe housing shortage in post-war Germany, for a few years the couple lived as subtenants at professor Hensel's place.
After leaving Marburg in 1928, Fraenkel taught at the University of Kiel for a year. He then made the fateful choice of accepting a position at the Hebrew University of Jerusalem, which had been founded four years earlier, where he spent the rest of his career. He became the first Dean of the Faculty of Mathematics, and for a while served as Rector of the University.
1922b. "The notion of 'definite' and the independence of the axiom of choice". In Jean van Heijenoort, 1967. From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931. Harvard University Press: 284-289.
1927. Zehn Vorlesungen über die Grundlegung der Mengenlehre. B. G. Teubner.
1930. "Georg Cantor". In Jahresbericht der Deutschen Mathematiker-Vereinigung 39, 189-266. Also appeared separately as Georg Cantor Leipzig: B. G. Teubner and is abridged in Cantor's Gesammelte Abhandlungen.
1930-1931 (5691). " ? ? ?". Part 1 in VI(8) 16-19, part 2 in VI(9). Reprinted together as a monograph by in 1931 Reprinted in 1987-8. Translated by Mark Zelcer in Hakirah vol. 12.
1930-1931b. "Die heutigen Gegensätze in der Grundlegung der Mathematik." In Erkenntnis vol. 1.
1945. " "? ? "? "? ". In Y. L. Fishman (ed.) ? ? ? ?, ? -?. Jerusalem Mossad HaRav Kook.
1946. "Address by Abraham A. Fraenkel". In Founder's Day: The Dropsie College for Hebrew and Cognate learning. Addresses: The Honorable Herbert H. Lehman, Professor Abraham Fraenkel. Philadelphia: Dropsie College.
1946. "The Recent Controversies about the Foundations of Mathematics". In Scripta Mathematica XII(4).
1947. "The Hebrew University and the Regulation of Secondary Education in Palestine". In Jewish Education 18:2.
1947. "The recent controversies about the foundation of mathematics". In Scripta Mathematica XIII, pp 17-36.
1953b. Abstract Set theory. Amsterdam: North Holland Publishing Co.
1955. Integers and the Theory of Numbers. New York: [Scripta Mathematica], Yeshiva University.
1955b. ." ? ?" In : ? ' . Y. Tirosh (ed.). Tel Aviv: Merkaz LeTarbut Shel HaPoel Mizrahi; 193-194.
1958. "? - ? ?". In Shimon Braunstein and Gershon Chorgon (eds.) ? ? . New York: Vaad HaYovel; 248-250.
1960. "Jewish mathematics and astronomy". In Scripta Mathematica XXV, pp 33-47. (Appeared in Hebrew in Tekhnika Umada, Tel Aviv, 1947. Footnote 12 of the Scripta Mathematica version claims that the essay was written in the 1930s.)
1960. "Epistemology and logic". In Synthese 12, pp. 333-337.
1961. Essays on the foundations of mathematics, dedicated to A. A. Fraenkel on his seventieth anniversary. Y. Bar-Hillel, E. I. J. Poznanski, M. O. Rabin and A. Robinson, eds. Jerusalem, the Hebrew University: Magnes Press.