Model theory and the philosophy of mathematical practice: formalization without foundationalism
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Cambridge, United Kingdom
Cambridge University Press
2018
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xi, 352 Seiten Illustrationen 26 cm |
| ISBN: | 9781107189218 |
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MARC
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Record in the Search Index
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| adam_text | Contents
List of Figures [page x]
Acknowledgments [xi]
Introduction [1]
PART I REFINING THE NOTION OF CATEGORICITY [29]
1 Formalization [31]
1.1 The Concept of Formalization [32]
1.2 Vocabulary and Structures [34]
1.3 Logics [41]
1.4 Theories and Axioms [47]
2 The Context of Formalization [31]
2.1 The Process of Formalization [51]
2.2 Two Roles of Formalization [54]
2.3 A Criterion for Evaluating Properties of Theories [58]
2.4 Virtuous Properties as an Organizing Principle [61]
3 Categoricity [68]
3.1 Categoricity of Second Order Theories [69]
3.2 L(ouco-categoricity [74]
3.3 Lo)yQ}: Categoricity in Power [78]
3.4 The Significance of Categoricity (in Power) [84]
PART II THE PARADIGM SHIFT [87]
4 What Was Model Theory About? [89]
4.1 The Downward Lowenheim-Skolem-Tarski Theorem [89]
4.2 Completeness, Compactness, and the Upward
Lowenheim-Skolem-Tarski Theorem [92]
4.3 Complete Theories [99]
4.4 Quantifier Complexity [104]
4.5 Interpretability [108]
4.6 What Is a Structure, Really? [Ill]
4.7 When Are Structures Equal’? [116]
vin
CONTENTS
5 What Is Contemporary Model Theory About? [119]
5.1 Analogy to Theorem to Method [119]
5.2 Universal Domains [124]
5.3 The Stability Hierarchy [128]
5.4 Combinatorial Geometry [133]
5.5 Classification: The Main Gap [137]
5.6 Why Is Model Theory So Entwined with
Classical Mathematics? [143]
6 Isolating Tame Mathematics [ 148]
6.1 Groups of Finite Morley Rank [149]
6.2 Formal Methods as a Tool in Mathematics [151]
6.3 First Order Analysis [156]
6.4 What Are the Central Notions of Model Theory? [162]
7 Infinitary Logic [167]
7.1 Categoricity in Uncountable Power for Lm }£0 [168]
7.2 The Vaught Conjecture [171]
7.3 Déjà vu: Categoricity in Infinitary Second Order Logic [175]
8 Model Theory and Set Theory [177]
8.1 Is There Model Theory without Axiomatic Set Theory? [178]
8.2 Is There Model Theory without Combinatorial Set Theory? [182]
8.3 Why Is K0 Exceptional for Model Theory? [186]
8.4 Entanglement of Model Theory and Cardinality [189]
8.5 Entanglement of Model Theory and the Replacement Axiom [192]
8.6 Entanglement of Model Theory with Extensions of ZFC [ 196]
8.7 Moral [198]
PART III GEOMETRY [201]
9 Axiomatization of Geometry [203]
9.1 The Goals of Axiomatization [205]
9.2 Descriptions of the Geometric Continuum [211]
9.3 Some Geometric Data Sets and Axiom Systems [217]
9.4 Geometry and Algebra [221]
9.5 Proportion and Area [229]
10 Tty Area, and Circumference of Circles [234]
10.1 7T in Euclidean and Archimedean Geometry [234]
10.2 From Descartes to Tarski [239]
10.3 n in Geometries over Real Closed Fields [243]
11 Complete: The Word for All Seasons [250]
11.1 Hilbert’s Continuity Axioms [252]
11.2 Against the Dedekind Postulate for Geometry [255]
CONTENTS
IX
PART IV METHODOLOGY [259]
12 Formalization and Purity in Geometry [261]
12.1 Content and Vocabulary [262]
12.2 Projective and Affine Geometry [265]
12-3 General Schemes for Characterizing Purity [267]
12.4 Modesty, Purity, and Generalization [273]
12.5 Purity and the Desargues Proposition [273]
12.6 Distinguishing Algebraic and Geometric Proof [281]
13 On the Nature of Definition: Model Theory [283]
13.1 Methodology of Classification [285]
13.2 The Fecundity of the Stability Hierarchy [287]
13.3 Dividing Lines [292]
13.4 Definition, Classification, and Taxonomy [294]
14 Formalism-Freeness (Mathematical Properties) [300]
15 Summation [312]
References [317]
Index [347]
|
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| illustrated | Illustrated |
| indexdate | 2024-07-10T08:20:14Z |
| institution | BVB |
| isbn | 9781107189218 |
| language | English |
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| physical | xi, 352 Seiten Illustrationen 26 cm |
| publishDate | 2018 |
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| publisher | Cambridge University Press |
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| spelling | Baldwin, John T. 1944- Verfasser (DE-588)128927690 aut Model theory and the philosophy of mathematical practice formalization without foundationalism John T. Baldwin (University of Illinois, Chicago) Cambridge, United Kingdom Cambridge University Press 2018 xi, 352 Seiten Illustrationen 26 cm txt rdacontent n rdamedia nc rdacarrier Modelltheorie (DE-588)4114617-7 gnd rswk-swf Formalisierung (DE-588)4123217-3 gnd rswk-swf Logik (DE-588)4036202-4 gnd rswk-swf Model theory Model theory / Philosophy Logic, Symbolic and mathematical Modelltheorie (DE-588)4114617-7 s Formalisierung (DE-588)4123217-3 s Logik (DE-588)4036202-4 s DE-604 ebook version 9781108103015 Digitalisierung BSB München - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030899381&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baldwin, John T. 1944- Model theory and the philosophy of mathematical practice formalization without foundationalism Modelltheorie (DE-588)4114617-7 gnd Formalisierung (DE-588)4123217-3 gnd Logik (DE-588)4036202-4 gnd |
| subject_GND | (DE-588)4114617-7 (DE-588)4123217-3 (DE-588)4036202-4 |
| title | Model theory and the philosophy of mathematical practice formalization without foundationalism |
| title_auth | Model theory and the philosophy of mathematical practice formalization without foundationalism |
| title_exact_search | Model theory and the philosophy of mathematical practice formalization without foundationalism |
| title_full | Model theory and the philosophy of mathematical practice formalization without foundationalism John T. Baldwin (University of Illinois, Chicago) |
| title_fullStr | Model theory and the philosophy of mathematical practice formalization without foundationalism John T. Baldwin (University of Illinois, Chicago) |
| title_full_unstemmed | Model theory and the philosophy of mathematical practice formalization without foundationalism John T. Baldwin (University of Illinois, Chicago) |
| title_short | Model theory and the philosophy of mathematical practice |
| title_sort | model theory and the philosophy of mathematical practice formalization without foundationalism |
| title_sub | formalization without foundationalism |
| topic | Modelltheorie (DE-588)4114617-7 gnd Formalisierung (DE-588)4123217-3 gnd Logik (DE-588)4036202-4 gnd |
| topic_facet | Modelltheorie Formalisierung Logik |
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