Model theory and the philosophy of mathematical practice: formalization without foundationalism
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge, United Kingdom
Cambridge University Press
2018
|
| Schlagwörter: | |
| Links: | 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 |
| Umfang: | xi, 352 Seiten Illustrationen 26 cm |
| ISBN: | 9781107189218 |
Internformat
MARC
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| 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 Cambridge, United Kingdom |b Cambridge University Press |c 2018 | |
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Datensatz im Suchindex
| _version_ | 1819379799413489664 |
|---|---|
| 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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| id | DE-604.BV045514963 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T18:29:06Z |
| institution | BVB |
| isbn | 9781107189218 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030899381 |
| oclc_num | 1028872683 |
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| owner | DE-12 |
| owner_facet | DE-12 |
| physical | xi, 352 Seiten Illustrationen 26 cm |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | Cambridge University Press |
| record_format | marc |
| 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 |
| url | 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 |
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