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Ernst Zermelo

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Ernst Friedrich Ferdinand Zermelo (July 27, 1871 - May 21, 1953) was a German logician and mathematician born in Berlin who died in Freiburg im Breisgau. His most significant contributions centered on set theory: in 1904 he proved the well-ordering theorem, that every set can be well ordered, and in 1908 he published a foundational axiomatization of set theory. His most enduring legacy is the Zermelo-Fraenkel axioms; although Zermelo developed the initial framework, Abraham Fraenkel and Thoralf Skolem independently expanded his axiom system in 1922 by adding the axioms of replacement and regularity, and the resulting system remains the most commonly used system for axiomatic set theory today. Beyond set theory, Zermelo also made notable contributions to game theory through his work on chess player rankings and introduced concepts including Zermelo's navigation problem, choice functions, and infinitary logic.

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Ernst Zermelo
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Attributed Works

Source Axiom of Infinity (Wikipedia)
Source Inaccessible cardinal (Wikipedia)
Source Wikipedia: Set (Mathematics)
Sets, Concepts
Source Wikipedia: Set (Mathematics)
Source Wikipedia: Von Neumann universe

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Source Ernst Zermelo (Wikipedia)

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Proofs Credited

Source Wolfram MathWorld: Envelope Theorem
Source Zermelo's Theorem (Game Theory) (Wikipedia)
Source MacTutor History of Mathematics, University of St Andrews: Ernst Zermelo - MacTutor History of Mathematics
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Source Ernst Zermelo (Wikipedia)
Sources
1. Ernst Zermelo (Wikipedia)
Wikimedia Foundation
  • Lead section, gender reference
    He is known for his role in developing Zermelo-Fraenkel axiomatic set theory and his proof of the well-ordering theorem.
  • In Branch: Logic and Foundations, Lead paragraph
    Ernst Friedrich Ferdinand Zermelo (; German: [tsɛɐ̯ˈmeːlo]; 27 July 1871-21 May 1953) was a German logician and mathematician, whose work has major implications for the foundations of mathematics.
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Ernst Zermelo (Wikipedia)
Lead section
Quote, Lead section
Ernst Friedrich Ferdinand Zermelo (; German: [tsɛɐ̯ˈmeːlo]; 27 July 1871 - 21 May 1953) was a German logician and mathematician, whose work has major implications for the foundations of mathematics.
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MacTutor History of Mathematics, University of St Andrews: Ernst Zermelo - MacTutor History of Mathematics
MacTutor History of Mathematics, University of St AndrewsProofs Credited: Zermelo's Well-Ordering Theorem, Biography
Quote, Proofs Credited: Zermelo's Well-Ordering Theorem, Biography
when he proved that every set can be well ordered
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Wikipedia: Von Neumann universe
Attributed Works: Von Neumann Universe, Lead sentence, attribution
Quote, Attributed Works: Von Neumann Universe, Lead sentence, attribution
it was first published by Ernst Zermelo in 1930
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Axiom of Infinity (Wikipedia)
Attributed Works: Axiom of Infinity, Lead sentence, attribution
Quote, Attributed Works: Axiom of Infinity, Lead sentence, attribution
It was first published by Ernst Zermelo as part of his set theory in 1908
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Inaccessible cardinal (Wikipedia)
Attributed Works: Inaccessible Cardinal, Lead sentence, attribution
Quote, Attributed Works: Inaccessible Cardinal, Lead sentence, attribution
Strongly inaccessible cardinals were introduced by Sierpiński & Tarski (1930) and Zermelo (1930)
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Zermelo's Theorem (Game Theory) (Wikipedia)
Wikimedia FoundationProofs Credited: Zermelo's Theorem (Game Theory), Lead
Quote, Proofs Credited: Zermelo's Theorem (Game Theory), Lead
The theorem is named after Ernst Zermelo, a German mathematician and logician, who proved the theorem for the example game of chess in 1913.
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Wolfram MathWorld: Envelope Theorem
Wolfram MathWorldProofs Credited: Envelope Theorem, Lead
Quote, Proofs Credited: Envelope Theorem, Lead
Proved in the general case by Darboux and Zermelo in 1894 and Kneser in 1898.
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Wikipedia: Set (Mathematics)
Wikimedia Foundation
  • Attributed Works: Sets, Lead
    Roster or enumeration notation is a notation introduced by Ernst Zermelo in 1908 that specifies a set by listing its elements between braces, separated by commas
  • Attributed Works: Set (mathematics), Lead
    Roster or enumeration notation is a notation introduced by Ernst Zermelo in 1908 that specifies a set by listing its elements between braces, separated by commas
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