The logical foundations of mathematics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford u.a.
Pergamon Press
1982
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | Foundations and philosophy of science and technology series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 320 S. graph. Darst. |
| ISBN: | 008025800X |
Internformat
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| 245 | 1 | 0 | |a The logical foundations of mathematics |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Oxford u.a. |b Pergamon Press |c 1982 | |
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Datensatz im Suchindex
| _version_ | 1804114655548801024 |
|---|---|
| adam_text | Contents
Chapter 1. First order Logic 1
Section 1. The sentential calculus 1
Section 2. Formalization 9
Section 3. The statement calculus as a formal system 13
Section 4. First order theories 19
Section 5. Models of first order theories 32
Section 6. Rules of logic; natural deduction 39
Section 7. First order theories with equality; variable binding term operators 57
Section 8. Completeness with vbtos 61
Section 9. An example of a first order theory 63
Chapter 2. The Origin of Modern Foundational Studies 68
Section 1. Mathematics as an independent science 68
Section 2. The arithmetization of analysis 69
Section 3. Constructivism 71
Section 4. Frege and the notion of a formal system 72
Section 5. Criteria for foundations 73
Chapter 3. Frege s System and the Paradoxes 76
Section 1. The intuitive basis of Frege s system 76
Section 2. Frege s system 78
Section 3. The theorem of infinity 90
Section 4. Criticisms of Frege s system 95
Section 5. The paradoxes 97
Section 6. Brouwer and intuitionism 98
Section 7. Poincar6 s notion of impredicative definition 100
Section 8. Russell s principle of vicious circle 101
Section 9. The logical paradoxes and the semantic paradoxes 102
Chapter 4. The Theory of Types 103
Section 1. Quantifying predicate letters 103
Section 2. Predicative type theory 105
Section 3. The development of mathematics in PT 116
Section 4. The system IT 120
Section 5. Criticisms of type theory as a foundation for mathematics 122
Section 6. The system ST 127
Section 7. Type theory and first order logic 130
ix
X CONTENTS
Chapter 5. Zermelo Fraenkel Set Theory 135
Section 1. Formalization of ZF 138
Section 2. The completing axioms 154
Section 3. Relations, functions, and simple recursion 159
Section 4. The axiom of choice 167
Section 5. The continuum hypothesis; descriptive set theory 170
Section 6. The systems of von Neumann Bernays Godel and Mostowski Kelley Morse 171
Section 7. Number systems; ordinal recursion 178
Section 8. Conway s numbers 186
Chapter 6. Hilbert s Program and Godel s Incompleteness Theorems 190
Section 1. Hilbert s program 193
Section 2. Godel s theorems and their import 193
Section 3. The method of proof of Godel s theorems; recursive functions 195
Section 4. Nonstandard models of S 207
Chapter 7. The Foundational Systems of W. V. Quine 213
Section 1. The system NF 213
Section 2. Cantor s theorem in NF 223
Section 3. The axiom of choice in NF and the theorem of infinity 226
Section 4. NF and ST; typical ambiguity 229
Section 5. Quine s system ML 233
Section 6. Further results on NF; variant systems 235
Section 7. Conclusions 236
Chapter 8. Categorical Algebra 237
Section 1. The notion of a category 238
Section 2. The first order language of categories 243
Section 3. Category theory and set theory 253
Section 4. Functors and large categories 255
Section 5. Formal development of the language and theory CS 260
Section 6. Topos theory 279
Section 7. Global elements in toposes 284
Section 8. Image factorizations and the axiom of choice 291
Section 9. A last look at CS 293
Section 10. ZF and WT 297
Section 11. The internal logic of toposes 302
Section 12. The internal language of a topos 306
Section 13. Conclusions 311
Selected Bibliography 313
Index 317
|
| any_adam_object | 1 |
| author | Hatcher, William S. 1935-2005 |
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| callnumber-subject | QA - Mathematics |
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| dewey-ones | 510 - Mathematics |
| dewey-raw | 510/.1 |
| dewey-search | 510/.1 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. ed. |
| format | Book |
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| isbn | 008025800X |
| language | English |
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| series2 | Foundations and philosophy of science and technology series |
| spelling | Hatcher, William S. 1935-2005 Verfasser (DE-588)1079636684 aut The logical foundations of mathematics 1. ed. Oxford u.a. Pergamon Press 1982 X, 320 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Foundations and philosophy of science and technology series Filosofia E Fundamentos Da Matematica larpcal Logica gtt Mathématiques - Philosophie Wiskunde gtt Logik Mathematik Philosophie Mathematics Philosophy Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Grundlage (DE-588)4158388-7 gnd rswk-swf Logik (DE-588)4036202-4 gnd rswk-swf Philosophie (DE-588)4045791-6 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s DE-604 Mathematik (DE-588)4037944-9 s Grundlage (DE-588)4158388-7 s Philosophie (DE-588)4045791-6 s Logik (DE-588)4036202-4 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000113668&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hatcher, William S. 1935-2005 The logical foundations of mathematics Filosofia E Fundamentos Da Matematica larpcal Logica gtt Mathématiques - Philosophie Wiskunde gtt Logik Mathematik Philosophie Mathematics Philosophy Mathematik (DE-588)4037944-9 gnd Mathematische Logik (DE-588)4037951-6 gnd Grundlage (DE-588)4158388-7 gnd Logik (DE-588)4036202-4 gnd Philosophie (DE-588)4045791-6 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4037951-6 (DE-588)4158388-7 (DE-588)4036202-4 (DE-588)4045791-6 |
| title | The logical foundations of mathematics |
| title_auth | The logical foundations of mathematics |
| title_exact_search | The logical foundations of mathematics |
| title_full | The logical foundations of mathematics |
| title_fullStr | The logical foundations of mathematics |
| title_full_unstemmed | The logical foundations of mathematics |
| title_short | The logical foundations of mathematics |
| title_sort | the logical foundations of mathematics |
| topic | Filosofia E Fundamentos Da Matematica larpcal Logica gtt Mathématiques - Philosophie Wiskunde gtt Logik Mathematik Philosophie Mathematics Philosophy Mathematik (DE-588)4037944-9 gnd Mathematische Logik (DE-588)4037951-6 gnd Grundlage (DE-588)4158388-7 gnd Logik (DE-588)4036202-4 gnd Philosophie (DE-588)4045791-6 gnd |
| topic_facet | Filosofia E Fundamentos Da Matematica Logica Mathématiques - Philosophie Wiskunde Logik Mathematik Philosophie Mathematics Philosophy Mathematische Logik Grundlage |
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