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Abstract set theory
281 pages, Hardcover
Published January 1, 1976
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About the author
Abraham A. Fraenkel
8 booksAbraham Adolf Halevi Fraenkel (Hebrew: אברהם הלוי אדולף פרנקל) 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-First World 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 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.
Fraenkel was a fervent Zionist and as such was a member of Jewish National Council and the Jewish Assembly of Representatives under the British mandate. He also belonged to the Mizrachi religious wing of Zionism, which promoted Jewish religious education and schools, and which advocated giving the Chief Rabbinate authority over marriage and divorce.
In 1919, he married Wilhelmina Malka A. Prins (1892–1983). Due to the severe housing shortage in post-First World 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 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.
Fraenkel was a fervent Zionist and as such was a member of Jewish National Council and the Jewish Assembly of Representatives under the British mandate. He also belonged to the Mizrachi religious wing of Zionism, which promoted Jewish religious education and schools, and which advocated giving the Chief Rabbinate authority over marriage and divorce.
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June 15, 2018
It is no secret among the mathematically inclined that there is "no getting around" Paul Halmos's Naive Set Theory, a very short book from a half-century ago that explains the principles of Zermelo-Fraenkel set theory in plain English; although we might all wish we were sharp enough not to have a use for it, it is agreed it is a fine thing to have on bookshelves generally. A further truth is that Abraham Fraenkel probably knew something about Zermelo-Fraenkel set theory, and his introductory English text on it, Abstract Set Theory, is a nice "mezzanine" introduction to more sophisticated thinking about sets (though it is a damnably hard thing to find a copy of).
As Shoenfield memorably pointed out "ZF" is not a hodgepodge of random principles that happen to make mathematics work out, and Frankel takes those of us with no especial mathematical gifts into the heart of the topic, really explaining how cardinals and ordinals are constructed and how to "reckon" with them. Perhaps it is the beginning of wisdom in mathematical science to realize that it is not about decoding a tapestry of symbols obscure to the common intellect, but more about making things "even out" intellectually, and Fraenkel's fine prose does help us make sense of such an approach to matters numerical.
As Shoenfield memorably pointed out "ZF" is not a hodgepodge of random principles that happen to make mathematics work out, and Frankel takes those of us with no especial mathematical gifts into the heart of the topic, really explaining how cardinals and ordinals are constructed and how to "reckon" with them. Perhaps it is the beginning of wisdom in mathematical science to realize that it is not about decoding a tapestry of symbols obscure to the common intellect, but more about making things "even out" intellectually, and Fraenkel's fine prose does help us make sense of such an approach to matters numerical.
Displaying 1 of 1 review