Philosophia Mathematica 2005 13(1):91-106; doi:10.1093/philmat/nki004
Philosophia Mathematica (III), Vol. 13 No. 1 © Oxford University Press, 2005, all rights reserved
Calixto Badesa. The Birth of Model Theory: Löwenheim's Theorem in the Frame of the Theory of Relatives Princeton: Princeton University Press, 2004. Pp. xiii + 240. ISBN 0–691–05853–9.
Ignacio Jané*
* Departament de Lògica, Història i Filosofia de la Ciència, Universitat de Barcelona 08028 Barcelona, Spain jane@ub.edu
| The first 150 words of the full text of this article appear below. |
When we encounter a theorem with a composite name, like Heine-Borel, Cantor-Bendixson, or Löwenheim-Skolem, we are curious to know what the particular contribution to it of each author actually was. The obvious guess is an alternative: either the first author provided a deficient or incomplete proof, or else the second author generalized the original theorem. As regards the Löwenheim-Skolem theorem, both things are the case. The theorem was first proved in 1915 by Leopold Löwenheim (1878–1957), and then reproved and generalized by Thoralf Skolem (1887–1963) in 1920, in 1922, and again in 1929. As stated by Löwenheim in 1915 and by Skolem in 1920, the theorem says that if a first-order sentence has a model, then it has a countable (finite or infinite) model. On the deficiencies of Löwenheim's proof something will be said later, but for now it is worth noting that in 1920 Skolem did not claim that . . . [Full Text of this Article]
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