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

In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in...

the additional contributions of Abraham Fraenkel, Zermelo set theory developed into the now-standard Zermelo–Fraenkel set theory (commonly known as ZFC...

Fränkel (or Fraenkel) is a surname. Notable people with the surname include: Abraham Fraenkel (1891–1965), German-Israeli mathematician, known for Zermelo–Fraenkel...

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

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)...

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...

single element is 0 {\displaystyle 0} . Within the framework of Zermelo–Fraenkel set theory, the axiom of regularity guarantees that no set is an element...

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

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

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

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...

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

defined models of set theory satisfying the axiom of limitation of size. Abraham Fraenkel and Azriel Lévy have stated that the axiom of limitation of size does...

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...

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...

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

ubiquitous in modern mathematics. Indeed, set theory, more specifically Zermelo–Fraenkel set theory, has been the standard way to provide rigorous foundations for...

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...

set theory described in axiomatic set theory by the axioms of Zermelo–Fraenkel set theory. Alternative set theories include: Vopěnka's alternative set...

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...

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

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...

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

{\displaystyle \{-1,1\}} . In many formal set theories, such as Zermelo–Fraenkel set theory, set builder notation is not part of the formal syntax of the...

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

continuum hypothesis and the axiom of choice are independent from Zermelo–Fraenkel set theory, for which he was awarded a Fields Medal. Cohen was born in...