The Birth of Model Theory (eBook)
by Calixto Badesa (Author)

 83,411 Words
 256 Pages
Löwenheim's theorem reflects a critical point in the history of mathematical logic, for it marks the birth of model theorythat is, the part of logic that concerns the relationship between formal theories and their models. However, while the original proofs of other, comparably significant theorems are well understood, this is not the case with Löwenheim's theorem. For example, the very result that scholars attribute to Löwenheim today is not the one that Skolema logician raised in the algebraic tradition, like Löwenheimappears to have attributed to him. In The Birth of Model Theory, Calixto Badesa provides both the first sustained, booklength analysis of Löwenheim's proof and a detailed description of the theoretical frameworkand, in particular, of the algebraic traditionthat made the theorem possible.
Badesa's three main conclusions amount to a completely new interpretation of the proof, one that sharply contradicts the core of modern scholarship on the topic. First, Löwenheim did not use an infinitary language to prove his theorem; second, the functional interpretation of Löwenheim's normal form is anachronistic, and inappropriate for reconstructing the proof; and third, Löwenheim did not aim to prove the theorem's weakest version but the stronger version Skolem attributed to him. This book will be of considerable interest to historians of logic, logicians, philosophers of logic, and philosophers of mathematics.
 Released: January 10, 2009
 Categories: Education
 Language: English
 Publisher: Princeton University Press
 ISBN10: 1400826187
 ISBN13: 9781400826186