Abraham Fraenkel information

Abraham Fraenkel (Hebrew: אברהם הלוי (אדולף) פרנקל; 17 February, 1891 – 15 October, 1965) was a German-born Israeli mathematician. He was an early Zionist...

theory, the axiom schema of replacement is a schema of axioms in Zermelo–Fraenkel set theory (ZF) that asserts that the image of any set under any definable...

In 1922, Abraham Fraenkel and Thoralf Skolem independently improved Zermelo's axiom system. The resulting system, now called Zermelo–Fraenkel axioms (ZF)...

mathematics. Mathematicians such as Gottlob Frege, Ernst Zermelo, Abraham Fraenkel, and Thoralf Skolem put much effort into revising set theory to eliminate...

Migash Yechezkel Landau Yaakov ben Moshe Levi Moelin Luis de Torres Abraham Fraenkel Shmuel Wosner Meir Abulafia Samuel ibn Naghrillah Yehuda Ashlag Yitzchok...

Vieweg, Braunschweig. Adolf Abraham Fraenkel 1923, Einleitung in die Mengenlehre, Springer, Berlin. Adolf Abraham Fraenkel, Y. Bar-Hillel, A. Levy 1984...

comprehension avoided Russell's paradox, several mathematicians including Zermelo, Fraenkel, and Gödel considered it the most important axiom of set theory. One instance...

philosophische Kritik, 91: 81–125 Reprinted in: Georg Cantor (1932), Adolf Fraenkel (Lebenslauf); Ernst Zermelo (eds.), Gesammelte Abhandlungen mathematischen...

of dependent choice is sufficient. Because there are models of Zermelo–Fraenkel set theory of interest to set theorists that satisfy the axiom of dependent...

implicitly about twenty years later by Ernst Zermelo and Abraham Fraenkel. Zermelo–Fraenkel set theory provided a series of principles that allowed for...

Georg Cantor Paul Cohen Richard Dedekind Paul Finsler Matthew Foreman Abraham Fraenkel Gottlob Frege Moti Gitik Kurt Gödel András Hajnal Felix Hausdorff Steve...

axiom of extension, or axiom of extent, is one of the axioms of Zermelo–Fraenkel set theory. Informally, it says that the two sets A and B are equal if...

Sets. Springer Verlag, 2nd ed., 1993, ISBN 0-387-94094-4, pp. 7–8 Abraham Adolf Fraenkel, Yehoshua Bar-Hillel, Azriel Lévy, Foundations of school Set Theory...

first three of these characterizations can be proven equivalent in Zermelo–Fraenkel set theory without the axiom of choice, but the equivalence of the third...

infinite. The existence of any other infinite set can be proved in Zermelo–Fraenkel set theory (ZFC), but only by showing that it follows from the existence...

philosophy that use it, the axiom of infinity is one of the axioms of Zermelo–Fraenkel set theory. It guarantees the existence of at least one infinite set, namely...

comprehension, or the axiom of regularity and axiom of pairing. In Zermelo–Fraenkel set theory, the axiom of regularity and axiom of pairing prevent any set...

including Joram Lindenstrauss (Johnson–Lindenstrauss lemma); Abraham Fraenkel (Zermelo–Fraenkel set theory); Shimshon Amitsur(Amitsur–Levitzki theorem); Saharon...

regularity. The axiom of replacement was first published in 1922 by Abraham Fraenkel and Thoralf Skolem, who had independently discovered that Zermelo's...

Set theorists Paul Bernays Georg Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell...

countably infinite, or has the cardinality of the real numbers." In Zermelo–Fraenkel set theory with the axiom of choice (ZFC), this is equivalent to the following...