Biography:Leopold Löwenheim
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Leopold Löwenheim | |
|---|---|
| Born | Krefeld, Germany |
| Died | May 5, 1957 (aged 78) |
| Alma mater | University of Berlin, Technical University Berlin |
| Known for | Löwenheim–Skolem theorem |
| Spouse(s) | Johanna Rassmussen |
| Scientific career | |
| Fields | Mathematical logic |
Leopold Löwenheim (26 June 1878 in Krefeld – 5 May 1957 in Berlin) was a Germany mathematician, known for his 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.
Important publications
- Leopold Löwenheim (1908). "Über das Auflösungsproblem im logischen Klassenkalkül". Sitzungsberichte der Berliner mathematischen Gesellschaft 7: 89–94. http://www.math.berlin/publikationen/sitzungsberichte.html.
- Leopold Löwenheim (1910). "Über die Auflösung von Gleichungen im logischen Gebietekalkül". Mathematische Annalen 68: 169–207. doi:10.1007/bf01474159. http://gdz.sub.uni-goettingen.de/download/PPN235181684_0068/PPN235181684_0068___LOG_0021.pdf.
- Leopold Löwenheim (1913). "Über Transformationen im Gebietekalkül". Mathematische Annalen 73: 245–272. doi:10.1007/bf01456715. http://gdz.sub.uni-goettingen.de/download/PPN235181684_0073/PPN235181684_0073___LOG_0024.pdf.
- Leopold Löwenheim (1915). "Über Möglichkeiten im Relativkalkül". Mathematische Annalen 76: 447–470. doi:10.1007/bf01458217. http://gdz.sub.uni-goettingen.de/download/PPN235181684_0076/PPN235181684_0076___LOG_0039.pdf. 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.
- Leopold Löwenheim (1915). "Über eine Erweiterung des Gebietekalküls, welche auch die gewöhnliche Algebra umfaßt". Archiv für systematische Philosophie 21: 137–148. http://www.digizeitschriften.de/dms/img/?PID=PPN827940653_0021.
- Leopold Löwenheim (1940). "Einkleidung der Mathematik in Schröderschen Relativkalkül". Journal of Symbolic Logic 5: 1–15. doi:10.2307/2269177.
- Leopold Löwenheim (1946). "On Making Indirect Proofs Direct". Scripta mathematica 12 (2): 125–147. Translated from German and published by Willard Van Orman Quine.
References
Further reading
- 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 links
- Löwenheim, Leopold at encyclopedia.com
- Christian Thiel (Nov 2007). "A Short Introduction to Löwenheim's Life and Work and to a Hitherto Unknown Paper". History and Philosophy of Logic 28: 289—302. doi:10.1080/01445340701708852. http://www.tandfonline.com/doi/pdf/10.1080/01445340701708852.
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