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Model theory and the philosophy of mathematical practice : formalization without foundationalism /
Major shifts in the field of model theory in the twentieth century have seen the development of new tools, methods, and motivations for mathematicians and philosophers. In this book, John T. Baldwin places the revolution in its historical context from the ancient Greeks to the last century, argues f...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York, NY :
Cambridge University Press,
2018.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Baldwin, John T., |e author. | |
| 245 | 1 | 0 | |a Model theory and the philosophy of mathematical practice : |b formalization without foundationalism / |c John T. Baldwin, University of Illinois, Chicago. |
| 264 | 1 | |a New York, NY : |b Cambridge University Press, |c 2018. | |
| 264 | 4 | |c ©2018 | |
| 300 | |a 1 online resource (xi, 352 pages) : |b illustrations | ||
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| 520 | |a Major shifts in the field of model theory in the twentieth century have seen the development of new tools, methods, and motivations for mathematicians and philosophers. In this book, John T. Baldwin places the revolution in its historical context from the ancient Greeks to the last century, argues for local rather than global foundations for mathematics, and provides philosophical viewpoints on the importance of modern model theory for both understanding and undertaking mathematical practice. The volume also addresses the impact of model theory on contemporary algebraic geometry, number theory, combinatorics, and differential equations. This comprehensive and detailed book will interest logicians and mathematicians as well as those working on the history and philosophy of mathematics. | ||
| 504 | |a Includes bibliographical references (pages 317-346) and index. | ||
| 505 | 0 | |6 880-01 |a Formalization -- The context of formalization -- Categoricity -- What was model theory about? -- What is contemporary model theory about? -- Isolating tame mathematics -- Infinitary logic -- Model theory and set theory -- Axiomatization of geometry -- Pi, area and circumference of circles -- Complete: the word for all seasons -- Formalization and purity in geometry -- On the nature of definition: model theory -- Formalism-freeness (mathematical properties) -- Summation. | |
| 588 | 0 | |a Print version record. | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Model theory. | |
| 650 | 0 | |a Logic, Symbolic and mathematical. | |
| 650 | 6 | |a Théorie des modèles. | |
| 650 | 6 | |a Logique symbolique et mathématique. | |
| 650 | 7 | |a MATHEMATICS |x General. |2 bisacsh | |
| 650 | 7 | |a Teoría de modelos |2 embne | |
| 650 | 7 | |a Lógica matemática |2 embne | |
| 650 | 7 | |a Logic, Symbolic and mathematical |2 fast | |
| 650 | 7 | |a Model theory |2 fast | |
| 776 | 0 | 8 | |i Print version: |a Baldwin, John T. |t Model theory and the philosophy of mathematical practice. |d Cambridge, United Kingdom : Cambridge University Press, 2018 |z 9781107189218 |w (OCoLC)1028239995 |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1694303 |z Texto completo |
| 880 | 0 | 0 | |6 505-01/(S |g Machine generated contents note: |g pt. I |t REFINING THE NOTION OF CATEGORICITY -- |g 1. |t Formalization -- |g 1.1. |t Concept of Formalization -- |g 1.2. |t Vocabulary and Structures -- |g 1.3. |t Logics -- |g 1.4. |t Theories and Axioms -- |g 2. |t Context of Formalization -- |g 2.1. |t Process of Formalization -- |g 2.2. |t Two Roles of Formalization -- |g 2.3. |t Criterion for Evaluating Properties of Theories -- |g 2.4. |t Virtuous Properties as an Organizing Principle -- |g 3. |t Categoricity -- |g 3.1. |t Categoricity of Second Order Theories -- |g 3.2. |t Lω1,ω-categoricity -- |g 3.3. |t Lω, ω: Categoricity in Power -- |g 3.4. |t Significance of Categoricity (in Power) -- |g pt. II |t PARADIGM SHIFT -- |g 4. |t What Was Model Theory About-- |g 4.1. |t Downward Lowenheim--Skolem--Tarski Theorem -- |g 4.2. |t Completeness, Compactness, and the Upward Lowenheim--Skolem--Tarski Theorem -- |g 4.3. |t Complete Theories -- |g 4.4. |t Quantifier Complexity -- |g 4.5. |t Interpretability -- |g 4.6. |t What Is a Structure, Really-- |g 4.7. |t When Are Structures Èqual'-- |g 5. |t What Is Contemporary Model Theory About-- |g 5.1. |t Analogy to Theorem to Method -- |g 5.2. |t Universal Domains -- |g 5.3. |t Stability Hierarchy -- |g 5.4. |t Combinatorial Geometry -- |g 5.5. |t Classification: The Main Gap -- |g 5.6. |t Why Is Model Theory So Entwined with Classical Mathematics-- |g 6. |t Isolating Tame Mathematics -- |g 6.1. |t Groups of Finite Morley Rank -- |g 6.2. |t Formal Methods as a Tool in Mathematics -- |g 6.3. |t First Order Analysis -- |g 6.4. |t What Are the Central Notions of Model Theory-- |g 7. |t Infinitary Logic -- |g 7.1. |t Categoricity in Uncountable Power for Lω1,ω -- |g 7.2. |t Vaught Conjecture -- |g 7.3. |t Deja vu: Categoricity in Infinitary Second Order Logic -- |g 8. |t Model Theory and Set Theory -- |g 8.1. |t Is There Model Theory without Axiomatic Set Theory-- |g 8.2. |t Is There Model Theory without Combinatorial Set Theory-- |g 8.3. |t Why Is α0 Exceptional for Model Theory-- |g 8.4. |t Entanglement of Model Theory and Cardinality -- |g 8.5. |t Entanglement of Model Theory and the Replacement Axiom -- |g 8.6. |t Entanglement of Model Theory with Extensions of ZFC -- |g 8.7. |t Moral -- |g pt. III |t GEOMETRY -- |g 9. |t Axiomatization of Geometry -- |g 9.1. |t Goals of Axiomatization -- |g 9.2. |t Descriptions of the Geometric Continuum -- |g 9.3. |t Some Geometric Data Sets and Axiom Systems -- |g 9.4. |t Geometry and Algebra -- |g 9.5. |t Proportion and Area -- |g 10. |t π, Area, and Circumference of Circles -- |g 10.1. |t π in Euclidean and Archimedean Geometry -- |g 10.2. |t From Descartes to Tarski -- |g 10.3. |t π in Geometries over Real Closed Fields -- |g 11. |t Complete: The Word for All Seasons -- |g 11.1. |t Hilbert's Continuity Axioms -- |g 11.2. |t Against the Dedekind Postulate for Geometry -- |g pt. IV |t METHODOLOGY -- |g 12. |t Formalization and Purity in Geometry -- |g 12.1. |t Content and Vocabulary -- |g 12.2. |t Projective and Affine Geometry -- |g 12.3. |t General Schemes for Characterizing Purity -- |g 12.4. |t Modesty, Purity, and Generalization -- |g 12.5. |t Purity and the Desargues Proposition -- |g 12.6. |t Distinguishing Algebraic and Geometric Proof -- |g 13. |t On the Nature of Definition: Model Theory -- |g 13.1. |t Methodology of Classification -- |g 13.2. |t Fecundity of the Stability Hierarchy -- |g 13.3. |t Dividing Lines -- |g 13.4. |t Definition, Classification, and Taxonomy -- |g 14. |t Formalism-Freeness (Mathematical Properties) -- |g 15. |t Summation. |
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