Leopold Löwenheim

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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

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]

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

Leopold was the son of Ludwig Löwenheim, a mathematics teacher at the polytechnic in Krefeld and Elizabeth Röhn, a writer. In 1881 the three of them left Krefeld first for Naples and then Berlin where Ludwig was a private scholar working on a comprehensive account of the influence of Democritus on modern science. Although he hoped this would gain him a teaching job at Humboldt University Ludwig died in 1894.[2]


  • 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. S2CID 122434845.
  • 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. S2CID 116581304. 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 reading[edit]

  • 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.

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