Über die Definition durch transfinite Induktion und verwandte Fragen der allgemeinen Mengenlehre

  title={{\"U}ber die Definition durch transfinite Induktion und verwandte Fragen der allgemeinen Mengenlehre},
  author={John von Neumann},
  journal={Mathematische Annalen},
  • J. Neumann
  • Published 1 December 1928
  • Mathematics
  • Mathematische Annalen
The Axioms of Zermelo–Fraenkel Set Theory
In the middle and late 19th century, members of the then small mathematical community began to look for a rigorous foundation of Mathematics, but at the time it was not clear what assumptions should be made and what operations should be allowed in mathematical reasoning.
The Mathematical Import of Zermelo's Well-Ordering Theorem
The seminal results of set theory are woven together in terms of a unifying mathematical motif, one whose transmutations serve to illuminate the historical development of the subject.
Über eine abgeschwächte Fassung des Auswahlaxioms
Der Unabhangigkeit des Auswahlaxioms sogar in diesem einfachsten Fall, ist vor langerer Zeit auf der Basis des Zermeloschen Axiomensystems der Mengenlehre nachgewiesen worden.
Gödel and Set Theory
The present account presents an integrated view of the historical and mathematical development as supported by Kurt Gödel's recently published lectures and correspondence, and finds the sustained motif of truth as formalizable in the “next higher system”.
Lectures on the Geometric Group Theory
Preface The main goal of this book is to describe several tools of the quasi-isometric rigidity and to illustrate them by presenting (essentially self-contained) proofs of several fundamental
ICLE Set theory and the analyst
This survey is motivated by specific questions arising in the similarities and contrasts between (Baire) category and (Lebesgue) measure—category-measure duality and non-duality, as it were. The bulk
The empty set, the singleton, and the ordered pair
The emergence of the empty set, the singleton, and the ordered pair as clear and elementary set-theoretic concepts serves as amotif that reflects and illuminates larger and more significant developments in mathematical logic.
Set Theory from Cantor to Cohen
  • A. Kanamori
  • Mathematics
    Sets and Extensions in the Twentieth Century
  • 2012
Geometric Group Theory
Geometry and topology Metric spaces Differential geometry Hyperbolic space Groups and their actions Median spaces and spaces with measured walls Finitely generated and finitely presented groups
The Mathematical Development of Set Theory from Cantor to Cohen
An account of the development of set theory from its beginnings through the creation of forcing based on contentions, with an avowedly Whiggish emphasis on the heritage that has been retained and developed by current set theory.


Untersuchungen über die Grundlagen der Mengenlehre. I
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