The Birth Of Model Theory
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Author |
: Calixto Badesa |
Publisher |
: |
Total Pages |
: 256 |
Release |
: 2009 |
ISBN-10 |
: OCLC:1102388597 |
ISBN-13 |
: |
Rating |
: 4/5 (97 Downloads) |
Synopsis The Birth of Model Theory by : Calixto Badesa
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 |
ISBN-10 |
: 9781400826186 |
ISBN-13 |
: 1400826187 |
Rating |
: 4/5 (86 Downloads) |
Synopsis The Birth of Model Theory by : Calixto Badesa
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 |
ISBN-10 |
: 0691058539 |
ISBN-13 |
: 9780691058535 |
Rating |
: 4/5 (39 Downloads) |
Synopsis The Birth of Model Theory by : Calixto Badesa
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 |
ISBN-10 |
: 9789400708129 |
ISBN-13 |
: 9400708122 |
Rating |
: 4/5 (29 Downloads) |
Synopsis A Guide to Classical and Modern Model Theory by : Annalisa Marcja
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 |
ISBN-10 |
: 9780387227344 |
ISBN-13 |
: 0387227342 |
Rating |
: 4/5 (44 Downloads) |
Synopsis Model Theory : An Introduction by : David Marker
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 |
: Princeton University Press |
Total Pages |
: 184 |
Release |
: 1966-06-21 |
ISBN-10 |
: 0691079293 |
ISBN-13 |
: 9780691079295 |
Rating |
: 4/5 (93 Downloads) |
Synopsis Continuous Model Theory by : Chen Chung Chang
This is a study of the theory of models with truth values in a compact Hausdorff topological space.
Author |
: Andrea Cappelli |
Publisher |
: Cambridge University Press |
Total Pages |
: 663 |
Release |
: 2012-04-12 |
ISBN-10 |
: 9780521197908 |
ISBN-13 |
: 0521197902 |
Rating |
: 4/5 (08 Downloads) |
Synopsis The Birth of String Theory by : Andrea Cappelli
Explores the early stages of the development of string theory; essential reading for physicists, historians and philosophers of science.
Author |
: C.C. Chang |
Publisher |
: Courier Corporation |
Total Pages |
: 674 |
Release |
: 2013-10-03 |
ISBN-10 |
: 9780486310954 |
ISBN-13 |
: 0486310957 |
Rating |
: 4/5 (54 Downloads) |
Synopsis Model Theory by : C.C. Chang
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 |
: Chen Chung Chang |
Publisher |
: North-Holland |
Total Pages |
: 584 |
Release |
: 1977 |
ISBN-10 |
: UVA:X001446046 |
ISBN-13 |
: |
Rating |
: 4/5 (46 Downloads) |
Synopsis Model Theory by : Chen Chung Chang
Since the second edition of this book (1977), Model Theory has changed radically, and is now concerned with fields such as classification (or stability) theory, nonstandard analysis, model-theoretic algebra, recursive model theory, abstract model theory, and model theories for a host of nonfirst order logics. Model theoretic methods have also had a major impact on set theory, recursion theory, and proof theory. This new edition has been updated to take account of these changes, while preserving its usefulness as a first textbook in model theory. Whole new sections have been added, as well as new exercises and references. A number of updates, improvements and corrections have been made to the main text.
Author |
: Michael Darwin Morley |
Publisher |
: MAA Press |
Total Pages |
: 216 |
Release |
: 1973 |
ISBN-10 |
: UCR:31210003030176 |
ISBN-13 |
: |
Rating |
: 4/5 (76 Downloads) |
Synopsis Studies in Model Theory by : Michael Darwin Morley