The Birth of Model Theory

Löwenheim's Theorem in the Frame of the Theory of Relatives

Calixto Badesa

240 pages, parution le 30/03/2004

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Résumé

Löwenheim'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 Löwenheim's theorem. For example, the very result that scholars attribute to Löwenheim today is not the one that Skolem--a logician raised in the algebraic tradition, like Löwenheim--appears to have attributed to him. In The Birth of Model Theory, Calixto Badesa provides both the first sustained, book-length analysis of Löwenheim'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, 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.

L'auteur - Calixto Badesa

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

Sommaire

Algebra of Classes and Prepositional Calculus
The Theory of Relatives
Changing the Order of Quantifiers
The Löwenheim Normal Form
Preliminaries to Löwenheim's Theorem
Löwenheim's Theorem

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	PAPIER
Éditeur(s)	Princeton University Press
Auteur(s)	Calixto Badesa
Parution	30/03/2004
Nb. de pages	240
Format	16 x 24
Couverture	Relié
Poids	505g
Intérieur	Noir et Blanc
EAN13	9780691058535
ISBN13	978-0-691-05853-5