Gödel's incompleteness theorems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Oxford Univ. Press
1992
|
| Schriftenreihe: | Oxford logic guides
19 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 139 S. |
| ISBN: | 0195046722 |
Internformat
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| 100 | 1 | |a Smullyan, Raymond M. |d 1919-2017 |e Verfasser |0 (DE-588)115668411 |4 aut | |
| 245 | 1 | 0 | |a Gödel's incompleteness theorems |c Raymond M. Smullyan |
| 264 | 1 | |a New York [u.a.] |b Oxford Univ. Press |c 1992 | |
| 300 | |a XIII, 139 S. | ||
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| 490 | 1 | |a Oxford logic guides |v 19 | |
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Datensatz im Suchindex
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| adam_text | Contents
I The General Idea Behind Godel s Proof 1
I. Abstract Forms of Godel s and Tarski s Theorems ... 5
II. Undecidable Sentences of £ 10
II Tarski s Theorem for Arithmetic 14
I. The Language Ce 14
§1. Syntactic Preliminaries 14
§2. The Notion of Truth in £# 17
§3. Arithmetic and arithmetic Sets and Relations. 19
II. Concatenation and Godel Numbering 20
§4. Concatenation to the Base b 20
§5. Godel Numbering 22
III. Tarski s Theorem 24
§6. Diagonalization and Godel Sentences 24
III The Incompleteness of Peano Arithmetic With Ex¬
ponentiation 28
I. The Axiom System P.E 28
§1. The Axiom System P.E 28
II. Arithmetization of the Axiom System 30
§2. Preliminaries 30
§3. Arithmetization of the Syntax of P.E 33
§4. Godel s Incompleteness Theorem for P. E.. . . 36
IV Arithmetic Without the Exponential 40
I. The Incompleteness of P.A 40
§3. Concatenation to a Prime Base 43
§4. The Finite Set Lemma 45
§5. Proof of Theorem E 46
§6. The Incompleteness of Peano Arithmetic. ... 49
II. More on Ei-Relations 50
xii Contents
V Godel s Proof Based on u -Consistency 56
I. Some Abstract Incompleteness Theorems 58
§1. A Basic Incompleteness Theorem 58
§2. The uj- Consistency Lemma 61
II. So-Completeness 66
§4. Some So-complete Subsystems of Peano Arith¬
metic 68
§6. The w-Incompleteness of P.A 73
VI Rosser Systems 75
§1. Some Abstract Incompleteness Theorems Af¬
ter Rosser 76
§2. A General Separation Principle 77
§3. Rosser s Undecidable Sentence 81
§4. The Godel and Rosser Sentences Compared. . . 82
§5. More on Separation 84
VII Shepherdson s Representation Theorems 86
§1. Shepherdson s Representation Theorem 86
§2. Exact Rosser Systems 90
§3. Some Variants of Rosser s Undecidable Sentence. 93
§4. A Strengthening of Shepherdson s Theorems . 96
VIII Definablity and Diagonalization 97
§1. Definability and Complete Representability. . . 97
§2. Strong Definability of Functions in S 98
§3. Strong Definablity of Recursive Functions in
(R) 100
§4. Fixed Points and Godel Sentences 102
§5. Truth Predicates 104
IX The Unprovability of Consistency 106
§1. Provability Predicates 106
§2. The Unprovability of Consistency 108
§3. Henkin Sentences and Lob s Theorem 109
X Some General Remarks on Provability and Truth 112
XI Self-Referential Systems 116
I. Logicians Who Reason About Themselves 116
§1. An Analogue of the Tarski-Godel Theorem. . . 116
§2. Normal and Stable Reasoners of Type 1 117
§3. Rosser Type Reasoners 120
Contents xiii
§4. The Consistency Problem 122
§5. Self-Futtlling Beliefs and Lob s Theorem. ... 124
II. Incompleteness Arguments in a General Setting .... 126
III. Systems of Type G 129
IV. Modal Systems 132
References 136
Index 138
|
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| id | DE-604.BV006633526 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:49:37Z |
| institution | BVB |
| isbn | 0195046722 |
| language | English |
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| physical | XIII, 139 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series | Oxford logic guides |
| series2 | Oxford logic guides |
| spelling | Smullyan, Raymond M. 1919-2017 Verfasser (DE-588)115668411 aut Gödel's incompleteness theorems Raymond M. Smullyan New York [u.a.] Oxford Univ. Press 1992 XIII, 139 S. txt rdacontent n rdamedia nc rdacarrier Oxford logic guides 19 Gödelscher Unvollständigkeitssatz (DE-588)4021417-5 gnd rswk-swf Gödelscher Unvollständigkeitssatz (DE-588)4021417-5 s DE-604 Oxford logic guides 19 (DE-604)BV000013997 19 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004241040&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Smullyan, Raymond M. 1919-2017 Gödel's incompleteness theorems Oxford logic guides Gödelscher Unvollständigkeitssatz (DE-588)4021417-5 gnd |
| subject_GND | (DE-588)4021417-5 |
| title | Gödel's incompleteness theorems |
| title_auth | Gödel's incompleteness theorems |
| title_exact_search | Gödel's incompleteness theorems |
| title_full | Gödel's incompleteness theorems Raymond M. Smullyan |
| title_fullStr | Gödel's incompleteness theorems Raymond M. Smullyan |
| title_full_unstemmed | Gödel's incompleteness theorems Raymond M. Smullyan |
| title_short | Gödel's incompleteness theorems |
| title_sort | godel s incompleteness theorems |
| topic | Gödelscher Unvollständigkeitssatz (DE-588)4021417-5 gnd |
| topic_facet | Gödelscher Unvollständigkeitssatz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004241040&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000013997 |
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