+612 9045 4394
The Birth of Model Theory : Loewenheim's Theorem in the Frame of the Theory of Relatives - Calixto Badesa

The Birth of Model Theory

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

Hardcover Published: 25th January 2004
ISBN: 9780691058535
Number Of Pages: 256
For Ages: 22+ years old

Share This Book:


RRP $174.00
or 4 easy payments of $31.06 with Learn more
Ships in 3 to 4 business days

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.

Industry Reviews

"A first-rate contribution to the history and philosophy of logic, this is scholarship at its best. It is, to my knowledge, the first book in the history of logic that focuses completely on a single result. Very original in approach and conception, it goes against the grain of much recent scholarship. Given the complexity of the subject, Badesa could not have done a better job of being clear and making the presentation accessible."--Paolo Mancosu, University of California, Berkeley
"The Birth of Model Theory represents a long overdue, in-depth analysis and exposition of one of the most important results in mathematical logic. There are hardly any informed, sustained treatments of L wenheim's work to be found in the literature. This well-written book should fill this gap."--Richard Zach, University of Calgary
"This book will be extremely useful to those seeking to make sense of L wenheim's work and those seeking to put it into its historical context. Calixto Badesa draws well-supported conclusions that contradict the entire modern body of scholarship on the topic."--Shaughan Lavine, University of Arizona

Prefacep. ix
Algebra of Classes and Propositional Calculusp. 1
Boolep. 1
Jevonsp. 10
Peircep. 12
Schroderp. 17
The Theory of Relativesp. 31
Introductionp. 31
Basic concepts of the theory of relativesp. 33
Basic postulates of the theory of relativesp. 40
Theory of relatives and model theoryp. 51
First-order logic of relativesp. 66
Changing the Order of Quantifiersp. 73
Schroder's proposalp. 73
Lowenheim's approachp. 81
The problem of expansionsp. 87
Skolem functionsp. 94
The Lowenheim Normal Formp. 107
The Lowenheim normal form of an equationp. 107
Comments on Lowenheim's methodp. 113
Conclusionsp. 122
Preliminaries to Lowenheim's Theoremp. 129
Indices and elementsp. 129
Types of indicesp. 132
Assignmentsp. 135
Types of equationsp. 138
Lowenheim's Theoremp. 143
The problemp. 143
An analysis of Lowenheim's proofp. 148
Reconstructing the proofp. 191
p. 207
Introductionp. 207
Syntaxp. 207
Semanticsp. 211
The Lowenheim normal formp. 217
Lowenheim's theoremp. 220
Referencesp. 227
Indexp. 237
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780691058535
ISBN-10: 0691058539
Audience: Tertiary; University or College
For Ages: 22+ years old
Format: Hardcover
Language: English
Number Of Pages: 256
Published: 25th January 2004
Publisher: Princeton University Press
Country of Publication: US
Dimensions (cm): 23.5 x 15.2  x 2.13
Weight (kg): 0.5