The birth of model theory : Lowenheim's theorem in the frame of the theory of relatives / Calixto Badesa ; translated by Michael Maudsley ; revised by the author.

Format:

Book

Author/Creator:

Badesa, Calixto.

Language:

English

Subjects (All):

Löwenheim, Leopold, 1878-1957.

Löwenheim, Leopold.

Logic, Symbolic and mathematical.

Physical Description:

1 online resource (255 pages)

Edition:

Course Book

Place of Publication:

Princeton, N.J. ; Oxford : Princeton University Press, c2004.

Language Note:

English

Summary:

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.

Contents:

Frontmatter

Contents

Preface

Chapter 1. Algebra of Classes and Propositional Calculus

Chapter 2. The Theory of Relatives

Chapter 3. Changing the Order of Quantifiers

Chapter 4. The Löwenheim Normal Form

Chapter 5. Preliminaries to Löwenheim's Theorem

Chapter 6. Löwenheim's Theorem

Appendix. First-Order Logic with Fleeing Indices

References

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786612607936

9781282607934

1282607936

9781400826186

1400826187

OCLC:

700686802