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...

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

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"...

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...

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...

namely a set containing the natural numbers. It was first published by Ernst Zermelo as part of his set theory in 1908. Using first-order logic primitive...

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...

{\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...

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...

Dámaso Berenguer, Spanish general and prime minister (b. 1873) May 21 – Ernst Zermelo, German logician and mathematician (b. 1871) May 30 – Dooley Wilson...

Cantor's theory of cardinality. In 1908, Ernst Zermelo proposed the first axiomatization of set theory, now called Zermelo set theory, primarily to support his...

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...

elements. Roster or enumeration notation is a notation introduced by Ernst Zermelo in 1908 that specifies a set by listing its elements between braces...

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

about the relation between the absolute and God. Georg Cantor (1932). Ernst Zermelo (ed.). 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...

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

who presented it in 1952, although it had already been studied by Ernst Zermelo in the 1920s. Applications of the model include the ranking of competitors...

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

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

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...

In set 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...

Ernst Zermelo (1871–1953), set theorist Ernst Ziegler (1894-1974), German actor Ernst Zündel (1939-2017), German neo-Nazi and Holocaust denier Ernst,...

Hilbert's students were Hermann Weyl, chess champion Emanuel Lasker, Ernst Zermelo, and Carl Gustav Hempel. John von Neumann was his assistant. At the...

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

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...

false. Ernst Zermelo gave a proof that every set could be well-ordered, a result Georg Cantor had been unable to obtain. To achieve the proof, Zermelo introduced...

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...