Gödel's theorems: a workbook on formalization
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Stuttgart u.a.
Teubner
1991
|
| Schriftenreihe: | Teubner-Texte zur Mathematik
122 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 292 S. graph. Darst. |
| ISBN: | 3815420237 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804118944487833600 |
|---|---|
| adam_text | TABLE OF CONTENTS
I MATHEMATICS AND FORMALIZATION 7
1. On the nature of mathematical problems 8
2. Formalization— Hilbert s Programme 11
3. Outlook towards the denouement 24
4. Tarski, Truth, and Liars 27
E. Exercises and notes 28
II SETTING THE STAGE 3 3
1. Elementary languages 35
2. Elementary structures 40
3. A Galois connection 47
4. Formalizations of elementary logic 52
5. On syntactic metatheory 61
6. Soundness and completeness 68
E. Exercises and notes . 75
III THE STRUCTURE OF ARITHMETIC 98
1. Categories, morphisms and diagrams— topoi 9 9
2. Calculating with NNO s 147
3. Peano structures and their arithmetic 152
E. Exercises and notes 159
IV FORMAL FRAGMENTS OF ARITHMETIC 16 8
1. Elementary predicates and the theories 169
2. Syntactic properties of the theories 171
3. Semantic properties of the theories 177
4. Expressibility 180
E. Exercises and notes 187
V RECURSIVE ARITHMETIC 190
1. Primitive recursive functions, a definition 192
2. A collection of primitive recursive functions 194
3. Primitive recursive closure operations 197
4. Chinese remainders, Godel s p-function and sequences ... 205
5. General versus primitive recursion 211
6. Partial recursion and recursive enumerations 214
7. The representation theorems 218
E. Exercises and notes 223
VI ARITHMETIZATION 23 2
1. Göldel numbering 233
2. Repercussions on recursion theory 238
3. Church s Thesis 243
E. Exercises and notes 244
VII INCOMPLETENESS AND UNDECIDABILITY 246
1. Godel sentences 249
2. Proof predicates and consistency 251
3. Diagonalization and Tarski s Lemma 258
4. Undecidability 263
E. Exercises and notes 265
VIII WINDING THINGS UP 271
1. Mathematical ruminations 27 3
2. Final observation 281
SOURCES AND TRANSLATIONS OF QUOTES 28 2
BIBLIOGRAPHY 283
INDEX 289
NOTATION 292
|
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| author | Huber-Dyson, Verena |
| author_facet | Huber-Dyson, Verena |
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| building | Verbundindex |
| bvnumber | BV004832369 |
| classification_rvk | CC 2600 SK 130 |
| ctrlnum | (OCoLC)299607319 (DE-599)BVBBV004832369 |
| discipline | Mathematik Philosophie |
| format | Book |
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| id | DE-604.BV004832369 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:18:21Z |
| institution | BVB |
| isbn | 3815420237 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002974269 |
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| physical | 292 S. graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Teubner |
| record_format | marc |
| series | Teubner-Texte zur Mathematik |
| series2 | Teubner-Texte zur Mathematik |
| spelling | Huber-Dyson, Verena Verfasser aut Gödel's theorems a workbook on formalization Verena Huber-Dyson Stuttgart u.a. Teubner 1991 292 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Teubner-Texte zur Mathematik 122 Formalisierung - Gödelscher Unvollständigkeitssatz - Gödelscher Vollständigkeitssatz Gödelscher Vollständigkeitssatz (DE-588)4284044-2 gnd rswk-swf Gödelscher Unvollständigkeitssatz (DE-588)4021417-5 gnd rswk-swf Formalisierung (DE-588)4123217-3 gnd rswk-swf Gödelscher Unvollständigkeitssatz (DE-588)4021417-5 s DE-604 Formalisierung (DE-588)4123217-3 s Gödelscher Vollständigkeitssatz (DE-588)4284044-2 s Teubner-Texte zur Mathematik 122 (DE-604)BV000012607 122 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002974269&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Huber-Dyson, Verena Gödel's theorems a workbook on formalization Teubner-Texte zur Mathematik Formalisierung - Gödelscher Unvollständigkeitssatz - Gödelscher Vollständigkeitssatz Gödelscher Vollständigkeitssatz (DE-588)4284044-2 gnd Gödelscher Unvollständigkeitssatz (DE-588)4021417-5 gnd Formalisierung (DE-588)4123217-3 gnd |
| subject_GND | (DE-588)4284044-2 (DE-588)4021417-5 (DE-588)4123217-3 |
| title | Gödel's theorems a workbook on formalization |
| title_auth | Gödel's theorems a workbook on formalization |
| title_exact_search | Gödel's theorems a workbook on formalization |
| title_full | Gödel's theorems a workbook on formalization Verena Huber-Dyson |
| title_fullStr | Gödel's theorems a workbook on formalization Verena Huber-Dyson |
| title_full_unstemmed | Gödel's theorems a workbook on formalization Verena Huber-Dyson |
| title_short | Gödel's theorems |
| title_sort | godel s theorems a workbook on formalization |
| title_sub | a workbook on formalization |
| topic | Formalisierung - Gödelscher Unvollständigkeitssatz - Gödelscher Vollständigkeitssatz Gödelscher Vollständigkeitssatz (DE-588)4284044-2 gnd Gödelscher Unvollständigkeitssatz (DE-588)4021417-5 gnd Formalisierung (DE-588)4123217-3 gnd |
| topic_facet | Formalisierung - Gödelscher Unvollständigkeitssatz - Gödelscher Vollständigkeitssatz Gödelscher Vollständigkeitssatz Gödelscher Unvollständigkeitssatz Formalisierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002974269&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000012607 |
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