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Author | : Calixto Badesa |
Publisher | : |
Total Pages | : 256 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : |
Download The Birth of Model Theory Book in PDF, ePub and Kindle
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.
Author | : Calixto Badesa |
Publisher | : Princeton University Press |
Total Pages | : 256 |
Release | : 2009-01-10 |
Genre | : Mathematics |
ISBN | : 1400826187 |
Download The Birth of Model Theory Book in PDF, ePub and Kindle
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.
Author | : Calixto Badesa |
Publisher | : Princeton University Press |
Total Pages | : 256 |
Release | : 2004-01-25 |
Genre | : Mathematics |
ISBN | : 9780691058535 |
Download The Birth of Model Theory Book in PDF, ePub and Kindle
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.
Author | : Annalisa Marcja |
Publisher | : Springer Science & Business Media |
Total Pages | : 377 |
Release | : 2012-09-10 |
Genre | : Philosophy |
ISBN | : 9400708122 |
Download A Guide to Classical and Modern Model Theory Book in PDF, ePub and Kindle
This volume is easily accessible to young people and mathematicians unfamiliar with logic. It gives a terse historical picture of Model Theory and introduces the latest developments in the area. It further provides 'hands-on' proofs of elimination of quantifiers, elimination of imaginaries and other relevant matters. The book is for trainees and professional model theorists, and mathematicians working in Algebra and Geometry.
Author | : David Marker |
Publisher | : Springer Science & Business Media |
Total Pages | : 342 |
Release | : 2006-04-06 |
Genre | : Mathematics |
ISBN | : 0387227342 |
Download Model Theory : An Introduction Book in PDF, ePub and Kindle
Assumes only a familiarity with algebra at the beginning graduate level; Stresses applications to algebra; Illustrates several of the ways Model Theory can be a useful tool in analyzing classical mathematical structures
Author | : Chen Chung Chang |
Publisher | : Courier Corporation |
Total Pages | : 674 |
Release | : 2012-01-01 |
Genre | : Mathematics |
ISBN | : 0486488217 |
Download Model Theory Book in PDF, ePub and Kindle
This bestselling textbook for higher-level courses was extensively revised in 1990 to accommodate developments in model theoretic methods. Topics include models constructed from constants, ultraproducts, and saturated and special models. 1990 edition.
Author | : Andrea Cappelli |
Publisher | : Cambridge University Press |
Total Pages | : 663 |
Release | : 2012-04-12 |
Genre | : Science |
ISBN | : 0521197902 |
Download The Birth of String Theory Book in PDF, ePub and Kindle
Explores the early stages of the development of string theory; essential reading for physicists, historians and philosophers of science.
Author | : Philipp Rothmaler |
Publisher | : CRC Press |
Total Pages | : 324 |
Release | : 2018-12-07 |
Genre | : Mathematics |
ISBN | : 0429668503 |
Download Introduction to Model Theory Book in PDF, ePub and Kindle
Model theory investigates mathematical structures by means of formal languages. So-called first-order languages have proved particularly useful in this respect. This text introduces the model theory of first-order logic, avoiding syntactical issues not too relevant to model theory. In this spirit, the compactness theorem is proved via the algebraically useful ultrsproduct technique (rather than via the completeness theorem of first-order logic). This leads fairly quickly to algebraic applications, like Malcev's local theorems of group theory and, after a little more preparation, to Hilbert's Nullstellensatz of field theory. Steinitz dimension theory for field extensions is obtained as a special case of a much more general model-theoretic treatment of strongly minimal theories. There is a final chapter on the models of the first-order theory of the integers as an abelian group. Both these topics appear here for the first time in a textbook at the introductory level, and are used to give hints to further reading and to recent developments in the field, such as stability (or classification) theory.
Author | : Chen Chung Chang |
Publisher | : Princeton University Press |
Total Pages | : 184 |
Release | : 1966-06-21 |
Genre | : Mathematics |
ISBN | : 9780691079295 |
Download Continuous Model Theory Book in PDF, ePub and Kindle
This is a study of the theory of models with truth values in a compact Hausdorff topological space.
Author | : Katrin Tent |
Publisher | : Cambridge University Press |
Total Pages | : 259 |
Release | : 2012-03-08 |
Genre | : Mathematics |
ISBN | : 052176324X |
Download A Course in Model Theory Book in PDF, ePub and Kindle
Concise introduction to current topics in model theory, including simple and stable theories.