Leopold Löwenheim

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Leopold Löwenheim (26 June 1878 in Krefeld – 5 May 1957 in Berlin) was a German mathematician doing work in mathematical logic. The Nazi regime forced him to retire because under the Nuremberg Laws he was considered only three quarters Aryan. In 1943 much of his work was destroyed during a bombing raid on Berlin. Nevertheless, he survived the Second World War, after which he resumed teaching mathematics.[1]

Leopold Löwenheim
Born(1878-06-26)June 26, 1878
DiedMay 5, 1957(1957-05-05) (aged 78)
Alma materUniversity of Berlin, Technical University Berlin
Known forLöwenheim–Skolem theorem
Spouse(s)Johanna Rassmussen
Scientific career
FieldsMathematical logic

Löwenheim (1915) gave the first proof of what is now known as the Löwenheim–Skolem theorem, often considered the starting point for model theory.


  • Löwenheim, Leopold (1908). "Über das Auflösungsproblem im logischen Klassenkalkül". Sitzungsberichte der Berliner Mathematischen Gesellschaft (in German). 7: 89–94.
  • Löwenheim, Leopold (1910). "Über die Auflösung von Gleichungen im logischen Gebietekalkül" (PDF). Mathematische Annalen (in German). 68 (2): 169–207. doi:10.1007/bf01474159.
  • Löwenheim, Leopold (1913). "Über Transformationen im Gebietekalkül" (PDF). Mathematische Annalen (in German). 73 (2): 245–272. doi:10.1007/bf01456715.
  • Löwenheim, Leopold (1915). "Über Möglichkeiten im Relativkalkül" (PDF). Mathematische Annalen (in German). 76 (4): 447–470. doi:10.1007/bf01458217. Translated as "On possibilities in the calculus of relatives" in Jean van Heijenoort, 1967. A Source Book in Mathematical Logic, 1879–1931. Harvard Univ. Press: 228–251.
  • Löwenheim, Leopold (1915). "Über eine Erweiterung des Gebietekalküls, welche auch die gewöhnliche Algebra umfaßt". Archiv für Systematische Philosophie (in German). 21: 137–148.
  • Löwenheim, Leopold (1940). "Einkleidung der Mathematik in Schröderschen Relativkalkül". Journal of Symbolic Logic (in German). 5 (1): 1–15. doi:10.2307/2269177. JSTOR 2269177.
  • Löwenheim, Leopold (1946). Translated by Willard Van Orman Quine. "On Making Indirect Proofs Direct". Scripta Mathematica. 12 (2): 125–147.


Further readingEdit

  • Brady, Geraldine, 2000. From Peirce to Skolem. North Holland. Contains a detailed exegesis of the proof in Löwenheim (1915), and discusses how Thoralf Skolem simplified that proof and extended the scope and generality of the theorem.

External linksEdit

  • Löwenheim, Leopold at encyclopedia.com
  • Thiel, Christian (November 2007). "A Short Introduction to Löwenheim's Life and Work and to a Hitherto Unknown Paper". History and Philosophy of Logic. 28 (4): 289–302. doi:10.1080/01445340701708852.