J. Kőnig’s Strings Gestalt

  • Arie HinkisEmail author
Part of the Science Networks. Historical Studies book series (SNHS, volume 45)


In response to Poincaré’s challenge, two more proofs of CBT were produced in 1906, by J. Kőnig and by Felix Bernstein. Both proofs were presented by Poincaré in sessions of the French Academy of Science. J. Kőnig’s paper was published in the proceedings of the academy for July 1906, and that of Bernstein in December 1906. In both papers CBT is called the Equivalence Theorem; J. Kőnig adds “of Mr. Cantor” and Bernstein “of set theory”. It is likely that the authors did not actually present their papers in person and that Poincaré merely presented the papers for publication in the proceedings. In this case the delivery of the papers to Poincaré was surely accompanied by some letter exchange between the authors and Poincaré but we know of none.


Equivalence Theorem Determined Element Lateral Partitioning Complete Induction Letter Exchange 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Banach S. Un théorème sur les transformation biunivoques. Fund Math. 1924;6:236–9.Google Scholar
  2. Couturat L. Pour la logistique. Revue de metaphysique et de moral. 1906;14:208–50.Google Scholar
  3. Dauben JW. Georg Cantor. His mathematics and the philosophy of the infinite. Cambridge MA: Harvard University Press; 1979. Reprinted by Princeton University Press; 1990.Google Scholar
  4. Ebbinghaus HD. Ernst Zermelo. An approach to his life and work. New York: Springer; 2007.zbMATHGoogle Scholar
  5. Fraenkel AA. Abstract set theory. 3rd ed. Amsterdam: North Holland; 1966.Google Scholar
  6. Franchella M. On the origins of Dénes Kőnig’s infinity lemma. Archive for History of Exact Sciences. 1997;51(1):3–27.MathSciNetzbMATHCrossRefGoogle Scholar
  7. Franchella M. Towards a re-evaluation of Julius Kőnig’s contribution to logic. The bulletin of symbolic logic. 2000;6(1):45–56.MathSciNetzbMATHCrossRefGoogle Scholar
  8. Grattan-Guinness I. The search for mathematical roots, 1870–1940: logics, set theories and the foundations of mathematics from Cantor through Russell and Gődel, Princeton University Press; 2000.Google Scholar
  9. Hessenberg G. Grundbegriffe der Mengenlehre. Abhandlungen der Friesschen Schule. 1906;2(1):479–706. reprinted Gőttingen, Vardenhoeck & Ruprecht 1906.Google Scholar
  10. Hilbert D. Über die Grundlagen der Logik und Arithmetic, Verhandlungen des Dritten Internationalen Mathematiker-Kongresses in Heidelberg vom 8. bis 13. August 1904;174–85. English translation: van Heijenhoort 1967. pp. 129–38.Google Scholar
  11. Jourdain PEB. On the transfinite cardinal numbers of well-ordered aggregates. Philosophical Magazine (6). 1904a;7(37):61–75.zbMATHCrossRefGoogle Scholar
  12. Jourdain PEB. On the comparison of aggregates. Quarterly Journal of Pure and Applied Mathematics. 1907b;38:352–67.Google Scholar
  13. Mańka R, Wojciechowska A. On two Cantorian theorems. Annals of the Polish Mathematical Society, Series II: Mathematical News. 1984;25:191–8.zbMATHGoogle Scholar
  14. Medvedev FA. 1966. Ранняя история теоремы эквивалентности (Early history of the equivalence theorem), Ист.-мат. исслед. (Research in the history of mathematics) 1966;17:229–46.Google Scholar
  15. Peano G. Super Theorema de Cantor-Bernstein, Rendiconti del Circulo Mathmatico di Palermo, 21:360–6. This printing is from May 1906. The paper was reprinted in Revista de Mathematica, 1906;8:136–57. The second printing is dated August 1906. The second printing contains an additional part titled “additione”.Google Scholar
  16. Peckhaus V. ‘Ich habe mich wohl gehütet alle patronen auf einmal zu verschiessen’; Ernst Zermelo in Gőttingen. History and Philosophy of Logic. 1990a;11:19–58.MathSciNetzbMATHCrossRefGoogle Scholar
  17. Poincaré H. “Les mathematiques et la logique”, part II. Revue de Métaphysique et de Morale. 1906a;14:17–34.Google Scholar
  18. Schoenflies A. Entwickelung der Mengenlehre und ihrer Anwendung. Leipzig: B. G. Teubner; 1913.Google Scholar
  19. Silver CL. Who invented Cantor’s back and forth argument? Modern Logic. 1994;4:74–8.MathSciNetzbMATHGoogle Scholar
  20. Whitehead AN, Russell B. Principia Mathematica, 3 vol, Cambridge University Press, 2nd ed. 1927. We refer to this book as PM.Google Scholar
  21. Zermelo E. Über die Addition transfiniter Cardinalzahlen, Nachrichten von der Kőniglich Gesellschaft der Wissenschaften zu Gőttingen, Mathematisch-Physikalische Klasse aus dem Jahre 1901;34–8.Google Scholar
  22. Zermelo E. Untersuchungen über die Grundlagen der Mengenlehre. I. Mathematische Annalen 1908b;65:261–81. English translation: van Heijenoort 1967. pp. 199–215.Google Scholar

Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.The Cohn Institute for the History and Philosophy of Science and IdeasTel Aviv UniversityTel AvivIsrael

Personalised recommendations