Ernst Friedrich Ferdinand Zermelo (/zɜːrˈmɛloʊ/, German: [tsɛɐ̯ˈmeːlo]; 27 July 1871 – 21 May 1953) was a German logician and mathematician, whose work...

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

named after Ernst Zermelo, a German mathematician and logician, who proved the theorem for the example game of chess in 1913. Zermelo's theorem can be...

Zermelo set theory (sometimes denoted by Z-), as set out in a seminal paper in 1908 by Ernst Zermelo, is the ancestor of modern Zermelo–Fraenkel set theory...

of choice (often called AC, see also Axiom of choice § Equivalents). Ernst Zermelo introduced the axiom of choice as an "unobjectionable logical principle"...

particular, Ernst Zermelo provided a construction that is nowadays only of historical interest, and is sometimes referred to as Zermelo ordinals. It...

is named after John von Neumann, although it was first published by Ernst Zermelo in 1930. The rank of a well-founded set is defined inductively as the...

discovered independently in 1899 by the German mathematician Ernst Zermelo. However, Zermelo did not publish the idea, which remained known only to David...

In mathematical optimization, Zermelo's navigation problem, proposed in 1931 by Ernst Zermelo, is a classic optimal control problem that deals with a...

{\displaystyle i\in I} . The axiom of choice was formulated in 1904 by Ernst Zermelo in order to formalize his proof of the well-ordering theorem. The axiom...

numbers. It was first published by Ernst Zermelo as part of his set theory in 1908. In the formal language of the Zermelo–Fraenkel axioms, the axiom is expressed...

about the relation between the absolute and God. Georg Cantor (1932). Ernst Zermelo (ed.). Gesammelte Abhandlungen mathematischen und philosophischen Inhalts...

equivalent to global choice rather than von Neumann's axiom. In 1930, Ernst Zermelo defined models of set theory satisfying the axiom of limitation of size...

axiom of union is one of the axioms of Zermelo–Fraenkel set theory. This axiom was introduced by Ernst Zermelo. Informally, the axiom states that for...

musician Ernst Zermelo, set theorist Ernst Ziegler (1894-1974), German actor Ernst Zündel (1939-2017), German neo-Nazi and Holocaust denier Ernst, pseudonym...

of Berlin, where his students included Lipót Fejér, Paul Koebe and Ernst Zermelo. In total, he advised at least 22 Ph. D students. In 1914 Schwarz's...

entire structure of mathematics. Mathematicians such as Gottlob Frege, Ernst Zermelo, Abraham Fraenkel, and Thoralf Skolem put much effort into revising...

Abhandlungen mathematischen und philosophischen Inhalts, Georg Cantor, ed. Ernst Zermelo, with biography by Adolf Fraenkel; orig. pub. Berlin: Verlag von Julius...

81–125 Reprinted in: Georg Cantor (1932), Adolf Fraenkel (Lebenslauf); Ernst Zermelo (eds.), Gesammelte Abhandlungen mathematischen und philosophischen Inhalts...

every value of x." He attributes the idea behind the proof to Cantor. Ernst Zermelo has a theorem (which he calls "Cantor's Theorem") that is identical...

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

{4, 2, 1, 3} B = {blue, white, red}. This notation was introduced by Ernst Zermelo in 1908. In a set, all that matters is whether each element is in it...

choice) but neither publishes his proof nor tells Cantor about it. Ernst Zermelo discovered Dedekind's proof and in 1908 he publishes his own proof based...

Cantor perceived himself as having been publicly humiliated. Although Ernst Zermelo demonstrated less than a day later that König's proof had failed, Cantor...

axiomatic set theory, especially his additions to Ernst Zermelo's axioms, which resulted in the Zermelo–Fraenkel set theory. Abraham Adolf Halevi Fraenkel...

Corporation. p. 27. ISBN 978-0-486-79549-2. Heinz-Dieter Ebbinghaus (2007). Ernst Zermelo: An Approach to His Life and Work. Springer Science & Business Media...

Zermelo's categoricity theorem was proven by Ernst Zermelo in 1930. It states that all models of a certain second-order version of the Zermelo-Fraenkel...

an emptiness predicate. Zermelo accepted O {\displaystyle O} itself as a set, but considered it an "improper set". In Zermelo set theory, the existence...

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

be 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...