Gödel's Incompleteness Theorems: a guided tour through Kurt Gödel’s historic proof
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Book |
| Language: | English |
| Published: |
Berlin
Springer
[2024]
|
| Edition: | 2025. Auflage |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | This book is a translation of the German edition "Die Gödel'schen Unvollständigkeitssätze", 2nd edition by Dirk W. Hoffmann. The translation was done with the help of artificial intelligence machine translation tool. |
| Physical Description: | XIX, 385 Seiten Illustrationen, Diagramme |
| ISBN: | 3662695499 9783662695494 |
Staff View
MARC
| LEADER | 00000nam a22000008c 4500 | ||
|---|---|---|---|
| 001 | BV049921880 | ||
| 003 | DE-604 | ||
| 005 | 20241126 | ||
| 007 | t| | ||
| 008 | 241023s2024 gw a||| |||| 00||| eng d | ||
| 015 | |a 24,N21 |2 dnb | ||
| 016 | 7 | |a 1329637844 |2 DE-101 | |
| 020 | |a 3662695499 |9 3-662-69549-9 | ||
| 020 | |a 9783662695494 |c : circa EUR 53.49 (DE) (freier Preis), circa EUR 54.99 (AT) (freier Preis), circa CHF 59.00 (freier Preis), circa EUR 49.99 |9 978-3-662-69549-4 | ||
| 024 | 3 | |a 9783662695494 | |
| 028 | 5 | 2 | |a Bestellnummer: 89279446 |
| 028 | 5 | 2 | |a Bestellnummer: 978-3-662-69549-4 |
| 035 | |a (OCoLC)1477619213 | ||
| 035 | |a (DE-599)DNB1329637844 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c XA-DE-BE | ||
| 049 | |a DE-29T | ||
| 084 | |a MAT 000 |2 stub | ||
| 084 | |8 1\p |a 510 |2 23sdnb | ||
| 100 | 1 | |a Hoffmann, Dirk W. |d 1972- |e Verfasser |0 (DE-588)122854802 |4 aut | |
| 245 | 1 | 0 | |a Gödel's Incompleteness Theorems |b a guided tour through Kurt Gödel’s historic proof |c Dirk W. Hoffmann |
| 264 | 1 | |a Berlin |b Springer |c [2024] | |
| 300 | |a XIX, 385 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a This book is a translation of the German edition "Die Gödel'schen Unvollständigkeitssätze", 2nd edition by Dirk W. Hoffmann. The translation was done with the help of artificial intelligence machine translation tool. | ||
| 650 | 0 | 7 | |a Gödelscher Unvollständigkeitssatz |0 (DE-588)4021417-5 |2 gnd |9 rswk-swf |
| 653 | |a Crisis of the foundations of mathematics | ||
| 653 | |a Gödel | ||
| 653 | |a Logic | ||
| 653 | |a provability | ||
| 653 | |a undecidability | ||
| 689 | 0 | 0 | |a Gödelscher Unvollständigkeitssatz |0 (DE-588)4021417-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | 2 | |a Hoffmann, Dirk W. |t Die Gödel'schen Unvollständigkeitssätze |f 2017 |
| 710 | 2 | |a Springer-Verlag GmbH |0 (DE-588)1065168780 |4 pbl | |
| 775 | 0 | 8 | |i Parallele Sprachausgabe |a Dirk W. Hoffmann |t Die Gödel'schen Unvollständigkeitssätze |d 2. Auflage |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-662-69550-0 |
| 856 | 4 | 2 | |m X:MVB |q text/html |u http://deposit.dnb.de/cgi-bin/dokserv?id=35f2f91ad8c14ed2948dc1b3e2a306ab&prov=M&dok_var=1&dok_ext=htm |3 Inhaltstext |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035260443&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 883 | 1 | |8 1\p |a vlb |d 20240516 |q DE-101 |u https://d-nb.info/provenance/plan#vlb | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-035260443 | |
Record in the Search Index
| _version_ | 1826212188045443072 |
|---|---|
| adam_text |
CONTENTS
1
INTRODUCTION
1
1.1
THE
AXIOMATIC
METHOD
.
1
1.2
FORMAL
SYSTEMS
.
6
1.3
METAMATHEMATICS
.
13
1.3.1
CONSISTENCY
.
15
1.3.1.1
PROOF
OF
CONSISTENCY
AT
THE
SEMANTICS
LEVEL
.
16
1.3.1.2
PROOF
OF
CONSISTENCY
AT
THE
SYNTAX
LEVEL
.
17
1.3.2
COMPLETENESS
.
18
1.3.3
HILBERT
'
S
PROGRAM
.
20
1.4
THE
INCOMPLETENESS
THEOREMS
.
26
1.4.1
THE
FIRST
INCOMPLETENESS
THEOREM
.
26
1.4.2
THE
SECOND
INCOMPLETENESS
THEOREM
.
28
1.5
ON
FORMALLY
UNDECIDABLE
PROPOSITIONS
.
28
2
FOUNDATIONS
OF
MATHEMATICS
33
2.1
THE
LOGICIST
PROGRAM
.
33
2.1.1
BEGRIFFSSCHRIFT
.
34
2.1.2
AXIOMS
OF
THE
BEGRIFFSSCHRIFT
.
37
2.1.3
FORMALIZATION
OF
ARITHMETIC
.
39
2.2
THE
NATURAL
NUMBERS
.
43
2.2.1
ARITHMETICES
PRINCIPIA
.
43
2.2.2
AXIOMS
OF
THE
ARITHMETICES
PRINCIPIA
.
46
2.2.3
DEDEKIND
'
S
ISOMORPHISM
THEOREM
.
50
2.3
PRINCIPIA
MATHEMATICA
.
56
2.3.1
CANTOR
'
S
THEOREM
.
60
2.3.2
RUSSELL
'
S
ANTINOMY
.
65
2.3.2.1
LOGICAL
FORMULATION
OF
THE
ANTINOMY
.
65
2.3.2.2
SET-THEORETIC
FORMULATION
OF
THE
ANTINOMY
.
.
68
2.3.2.3
IN
RUINS
.
69
2.3.3
TYPE
THEORY
.
73
2.3.4
THE
LOGIC
OF
THE
PRINCIPIA
MATHEMATICA
.
77
2.4
AXIOMATIC
SET
THEORY
.
86
2.4.1
CONTINUUM
HYPOTHESIS
.
87
2.4.2
WELL-ORDERING
THEOREM
.
90
2.4.3
CRITICISM
OF
ZERMELO
'
S
PROOF
.
99
2.4.3.1
THE
AXIOM
OF
CHOICE
.
99
2.4.3.2
NON-PREDICATIVE
DEFINITIONS
.
101
XVIII
CONTENTS
2.4.4
ZERMELO
'
S
AXIOMS
.
102
3
PROOF
SKETCH
109
3.1
ARITHMETIC
FORMULAS
.
110
3.2
THE
ARITHMETIZATION
OF
SYNTAX
.
117
3.3
I
AM
UNPROVABLE!
.
122
3.4
GODEL,
RICHARD
AND
THE
LIAR
.
129
3.4.1
THE
LIAR
PARADOX
.
130
3.4.2
RICHARD
'
S
ANTINOMY
.
132
3.4.3
WHEN
IS
A
FORMAL
SYSTEM
AFFECTED?
.
134
4
SYSTEM
P
139
4.1
SYNTAX
.
140
4.1.1
TERMS
AND
FORMULAS
.
142
4.1.2
SUBSTITUTIONS
.
148
4.2
SEMANTICS
.
150
4.2.1
DEFINITION
OF
EQUALITY
.
154
4.2.2
DEFINITION
OF
NATURAL
NUMBERS
.
155
4.3
AXIOMS
AND
INFERENCE
RULES
.
156
4.4
FORMAL
PROOFS
.
162
4.4.1
PROPOSITIONAL
LOGIC
THEOREMS
.
166
4.4.2
HYPOTHESIS-BASED
PROVING
.
178
4.4.3
PREDICATE
LOGIC
THEOREMS
.
182
4.4.4
THEOREMS
ABOUT
EQUALITY
.
185
4.4.5
NUMERICAL
THEOREMS
.
190
4.5
THE
ARITHMETIZATION
OF
SYNTAX
.
200
5
PRIMITIVE-RECURSIVE
FUNCTIONS
209
5.1
DEFINITION
AND
PROPERTIES
.
209
5.2
PRIMITIVE-RECURSIVE
FUNCTIONS
AND
RELATIONS
.
228
5.3
DECISION
PROCEDURES
.
274
5.4
THEOREM
V
.
279
6
THE
LIMITS
OF
MATHEMATICS
293
6.1
GODEL'S
MAIN
RESULT
.
293
6.1.1
INCOMPLETENESS
OF
SYSTEM
P
.
296
6.1.2
CONSEQUENCES
OF
THE
MAIN
RESULT
.
305
6.2
THE
FIRST
INCOMPLETENESS
THEOREM
.
315
6.2.1
INCOMPLETENESS
OF
ARITHMETIC
.
315
6.2.2
IMPLICATIONS
FOR
THE
RESTRICTED
FUNCTION
CALCULUS
.
330
6.2.2.1
SYNTAX
OF
FIRST-ORDER
PREDICATE
LOGIC
.
330
6.2.2.2
SEMANTICS
OF
FIRST-ORDER
PREDICATE
LOGIC
.
.
.
332
6.3
THE
SECOND
INCOMPLETENESS
THEOREM
.
352
7
EPILOGUE
363
CONTENTS
XIX
BIBLIOGRAPHY
365
IMAGE
CREDITS
373
NAME
INDEX
375
INDEX
379 |
| any_adam_object | 1 |
| author | Hoffmann, Dirk W. 1972- |
| author2 | Hoffmann, Dirk W. |
| author2_role | |
| author2_variant | d w h dw dwh |
| author_GND | (DE-588)122854802 |
| author_facet | Hoffmann, Dirk W. 1972- Hoffmann, Dirk W. |
| author_role | aut |
| author_sort | Hoffmann, Dirk W. 1972- |
| author_variant | d w h dw dwh |
| building | Verbundindex |
| bvnumber | BV049921880 |
| classification_tum | MAT 000 |
| ctrlnum | (OCoLC)1477619213 (DE-599)DNB1329637844 |
| discipline | Mathematik |
| edition | 2025. Auflage |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a22000008c 4500</leader><controlfield tag="001">BV049921880</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20241126</controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">241023s2024 gw a||| |||| 00||| eng d</controlfield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">24,N21</subfield><subfield code="2">dnb</subfield></datafield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">1329637844</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3662695499</subfield><subfield code="9">3-662-69549-9</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783662695494</subfield><subfield code="c">: circa EUR 53.49 (DE) (freier Preis), circa EUR 54.99 (AT) (freier Preis), circa CHF 59.00 (freier Preis), circa EUR 49.99</subfield><subfield code="9">978-3-662-69549-4</subfield></datafield><datafield tag="024" ind1="3" ind2=" "><subfield code="a">9783662695494</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">Bestellnummer: 89279446</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">Bestellnummer: 978-3-662-69549-4</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1477619213</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DNB1329637844</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">XA-DE-BE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-29T</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="8">1\p</subfield><subfield code="a">510</subfield><subfield code="2">23sdnb</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Hoffmann, Dirk W.</subfield><subfield code="d">1972-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)122854802</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Gödel's Incompleteness Theorems</subfield><subfield code="b">a guided tour through Kurt Gödel’s historic proof</subfield><subfield code="c">Dirk W. Hoffmann</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin</subfield><subfield code="b">Springer</subfield><subfield code="c">[2024]</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIX, 385 Seiten</subfield><subfield code="b">Illustrationen, Diagramme</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">This book is a translation of the German edition "Die Gödel'schen Unvollständigkeitssätze", 2nd edition by Dirk W. Hoffmann. The translation was done with the help of artificial intelligence machine translation tool.</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Gödelscher Unvollständigkeitssatz</subfield><subfield code="0">(DE-588)4021417-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Crisis of the foundations of mathematics</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Gödel</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Logic</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">provability</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">undecidability</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Gödelscher Unvollständigkeitssatz</subfield><subfield code="0">(DE-588)4021417-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2="2"><subfield code="a">Hoffmann, Dirk W.</subfield><subfield code="t">Die Gödel'schen Unvollständigkeitssätze</subfield><subfield code="f">2017</subfield></datafield><datafield tag="710" ind1="2" ind2=" "><subfield code="a">Springer-Verlag GmbH</subfield><subfield code="0">(DE-588)1065168780</subfield><subfield code="4">pbl</subfield></datafield><datafield tag="775" ind1="0" ind2="8"><subfield code="i">Parallele Sprachausgabe</subfield><subfield code="a">Dirk W. Hoffmann</subfield><subfield code="t">Die Gödel'schen Unvollständigkeitssätze</subfield><subfield code="d">2. Auflage</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-3-662-69550-0</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">X:MVB</subfield><subfield code="q">text/html</subfield><subfield code="u">http://deposit.dnb.de/cgi-bin/dokserv?id=35f2f91ad8c14ed2948dc1b3e2a306ab&prov=M&dok_var=1&dok_ext=htm</subfield><subfield code="3">Inhaltstext</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">DNB Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035260443&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">vlb</subfield><subfield code="d">20240516</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#vlb</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-035260443</subfield></datafield></record></collection> |
| id | DE-604.BV049921880 |
| illustrated | Illustrated |
| indexdate | 2025-03-10T13:00:59Z |
| institution | BVB |
| institution_GND | (DE-588)1065168780 |
| isbn | 3662695499 9783662695494 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035260443 |
| oclc_num | 1477619213 |
| open_access_boolean | |
| owner | DE-29T |
| owner_facet | DE-29T |
| physical | XIX, 385 Seiten Illustrationen, Diagramme |
| publishDate | 2024 |
| publishDateSearch | 2024 |
| publishDateSort | 2024 |
| publisher | Springer |
| record_format | marc |
| spelling | Hoffmann, Dirk W. 1972- Verfasser (DE-588)122854802 aut Gödel's Incompleteness Theorems a guided tour through Kurt Gödel’s historic proof Dirk W. Hoffmann Berlin Springer [2024] XIX, 385 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier This book is a translation of the German edition "Die Gödel'schen Unvollständigkeitssätze", 2nd edition by Dirk W. Hoffmann. The translation was done with the help of artificial intelligence machine translation tool. Gödelscher Unvollständigkeitssatz (DE-588)4021417-5 gnd rswk-swf Crisis of the foundations of mathematics Gödel Logic provability undecidability Gödelscher Unvollständigkeitssatz (DE-588)4021417-5 s DE-604 Hoffmann, Dirk W. Die Gödel'schen Unvollständigkeitssätze 2017 Springer-Verlag GmbH (DE-588)1065168780 pbl Parallele Sprachausgabe Dirk W. Hoffmann Die Gödel'schen Unvollständigkeitssätze 2. Auflage Erscheint auch als Online-Ausgabe 978-3-662-69550-0 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=35f2f91ad8c14ed2948dc1b3e2a306ab&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035260443&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p vlb 20240516 DE-101 https://d-nb.info/provenance/plan#vlb |
| spellingShingle | Hoffmann, Dirk W. 1972- Gödel's Incompleteness Theorems a guided tour through Kurt Gödel’s historic proof Gödelscher Unvollständigkeitssatz (DE-588)4021417-5 gnd |
| subject_GND | (DE-588)4021417-5 |
| title | Gödel's Incompleteness Theorems a guided tour through Kurt Gödel’s historic proof |
| title_alt | Die Gödel'schen Unvollständigkeitssätze |
| title_auth | Gödel's Incompleteness Theorems a guided tour through Kurt Gödel’s historic proof |
| title_exact_search | Gödel's Incompleteness Theorems a guided tour through Kurt Gödel’s historic proof |
| title_full | Gödel's Incompleteness Theorems a guided tour through Kurt Gödel’s historic proof Dirk W. Hoffmann |
| title_fullStr | Gödel's Incompleteness Theorems a guided tour through Kurt Gödel’s historic proof Dirk W. Hoffmann |
| title_full_unstemmed | Gödel's Incompleteness Theorems a guided tour through Kurt Gödel’s historic proof Dirk W. Hoffmann |
| title_short | Gödel's Incompleteness Theorems |
| title_sort | godel s incompleteness theorems a guided tour through kurt godel s historic proof |
| title_sub | a guided tour through Kurt Gödel’s historic proof |
| topic | Gödelscher Unvollständigkeitssatz (DE-588)4021417-5 gnd |
| topic_facet | Gödelscher Unvollständigkeitssatz |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=35f2f91ad8c14ed2948dc1b3e2a306ab&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035260443&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hoffmanndirkw godelsincompletenesstheoremsaguidedtourthroughkurtgodelshistoricproof AT springerverlaggmbh godelsincompletenesstheoremsaguidedtourthroughkurtgodelshistoricproof |