The Birth of Model Theory: Lowenheim's Theorem in the Frame of the Theory of Relatives - Couverture rigide

Badesa, Calixto

Couverture rigide

ISBN 10 : 0691058539 ISBN 13 : 9780691058535

Editeur : Princeton University Press, 2004

Synopsis

Lowenheim's theorem reflects a critical point in the history of mathematical logic, for it marks the birth of model theory--that 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 Lowenheim's theorem. For example, the very result that scholars attribute to Lowenheim today is not the one that Skolem--a logician raised in the algebraic tradition, like Lowenheim--appears to have attributed to him. In The Birth of Model Theory, Calixto Badesa provides both the first sustained, book-length analysis of Lowenheim's proof and a detailed description of the theoretical framework--and, in particular, of the algebraic tradition--that 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, Lowenheim did not use an infinitary language to prove his theorem; second, the functional interpretation of Lowenheim's normal form is anachronistic, and inappropriate for reconstructing the proof; and third, Lowenheim 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.

A propos du livre

À propos de l?auteur

Calixto Badesa is Associate Professor of Logic and History of Logic at the University of Barcelona.

Détails de l'édition

• Éditeur: Princeton University Press
• Date d'édition: 2004
• Langue: anglais
• ISBN 10: 0691058539
• ISBN 13: 9780691058535
• Reliure: Relié
• Nombre de pages: 256
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible