Labyrinth of thought: a history of set theory and its role in modern mathematics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
1999
|
| Schriftenreihe: | Science networks
23 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXI, 440 S. Ill., graph. Darst. |
| ISBN: | 3764357495 0817657495 |
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| 100 | 1 | |a Ferreirós Domínguez, José |e Verfasser |0 (DE-588)121021351 |4 aut | |
| 245 | 1 | 0 | |a Labyrinth of thought |b a history of set theory and its role in modern mathematics |c José Ferreirós |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 1999 | |
| 300 | |a XXI, 440 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Science networks |v 23 | |
| 648 | 7 | |a Geschichte 1850-1940 |2 gnd |9 rswk-swf | |
| 650 | 4 | |a Ensembles, Théorie des - Histoire | |
| 650 | 7 | |a Teoria dos conjuntos (história) |2 larpcal | |
| 650 | 7 | |a Verzamelingen (wiskunde) |2 gtt | |
| 650 | 4 | |a Geschichte | |
| 650 | 4 | |a Set theory |x History | |
| 650 | 0 | 7 | |a Geschichte |0 (DE-588)4020517-4 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1805068264079884288 |
|---|---|
| adam_text |
CONTENTS
INTRODUCTION
.
XI
1.
AIMS
AND
SCOPE
.
XIII
2.
GENERAL
HISTORIOGRAPHICAL
REMARKS
.
XVII
PART
ONE:
THE
EMERGENCE
OF
SETS
WITHIN
MATHEMATICS
.
1
I
INSTITUTIONAL
AND
INTELLECTUAL
CONTEXTS
IN
GERMAN
MATHEMATICS,
1800-1870
.
3
1.
MATHEMATICS
AT
THE
REFORMED
GERMAN
UNIVERSITIES
.
4
2.
TRADITIONAL
AND
'
MODEM
'
FOUNDATIONAL
VIEWPOINTS
.
10
3.
THE
ISSUE
OF
THE
INFINITE
.
18
4.
THE
GOTTINGEN
GROUP,
1855-1859
.
24
5.
THE
BERLIN
SCHOOL,
1855-1870
.
32
II
A
NEW
FUNDAMENTAL
NOTION:
RIEMANN
'
S
MANIFOLDS
.
39
L.THE
HISTORICAL
CONTEXT:
GROSSENLEHRE,
GAUSS,
AND
HERBART
.
41
2.
LOGICAL
PREREQUISITES
.
47
3.
THE
MATHEMATICAL
CONTEXT
OF
RIEMANN
'
S
INNOVATION
.
53
4.
RIEMANN
'
S
GENERAL
DEFINITION
.
62
5.
MANIFOLDS,
ARITHMETIC,
AND
TOPOLOGY
.
67
6.
RIEMANN
'
S
INFLUENCE
ON
THE
DEVELOPMENT
OF
SET
THEORY
.
70
APPENDIX:
RIEMANN
AND
DEDEKIND
.
77
III
DEDEKIND
AND
THE
SET-THEORETICAL
APPROACH
TO
ALGEBRA
.
81
L.THE
ALGEBRAIC
ORIGINS
OF
DEDEKIND
'
S
SET
THEORY,
1856-58
.
82
2.
A
NEW
FUNDAMENTAL
NOTION
FOR
ALGEBRA:
FIELDS
.
90
3.
THE
EMERGENCE
OF
ALGEBRAIC
NUMBER
THEORY
.
94
CONTENTS
VII
4.
IDEALS
AND
METHODOLOGY
.
99
5.
DEDEKIND
'
S
INFMITISM
.
107
6.
THE
DIFFUSION
OF
DEDEKIND
'
S
VIEWS
.
111
IV
THE
REAL
NUMBER
SYSTEM
.
117
1.
'
CONSTRUCTION
'
VS.
AXIOMATIZATION
.
119
2.
THE
DEFINITIONS
OF
THE
REAL
NUMBERS
.
124
3.
THE
INFLUENCE
OF
RIEMANN:
CONTINUITY
IN
ARITHMETIC
AND
GEOMETRY
.
135
4.
ELEMENTS
OF
THE
TOPOLOGY
OF
DR
.
137
V
ORIGINS
OF
THE
THEORY
OF
POINT-SETS
.
145
1.
DIRICHLET
AND
RIEMANN:
TRANSFORMATIONS
IN
THE
THEORY
OF
REAL
FUNCTIONS
.
147
2.
LIPSCHITZ
AND
HANKEL
ON
NOWHERE
DENSE
SETS
AND
INTEGRATION
.
154
3.
CANTOR
ON
SETS
OF
THE
FIRST
SPECIES
.
157
4.
NOWHERE
DENSE
SETS
OF
THE
SECOND
SPECIES
.
161
5.
CRYSTALLIZATION
OF
THE
NOTION
OF
CONTENT
.
165
PART
TWO:
ENTERING
THE
LABYRINTH
-
TOWARD
ABSTRACT
SET
THEORY
.
169
VI
THE
NOTION
OF
CARDINALITY
AND
THE
CONTINUUM
HYPOTHESIS
.
171
1.
THE
RELATIONS
AND
CORRESPONDENCE
BETWEEN
CANTOR
AND
DEDEKIND
.
172
2.NON-DENUMERABILITY
OF
DR
.
176
3.CAMOR
'
S
EXPOSITION
AND
THE
'
BERLIN
CIRCUMSTANCES'
.
183
4.EQUIPOLLENCE
OF
CONTINUA
DR
AND
IB"
.
187
5.
CANTOR
'
S
DIFFICULTIES
.
197
6.
DERIVED
SETS
AND
CARDINALITIES
.
202
7.
CANTOR
'
S
DEFINITION
OF
THE
CONTINUUM
.
208
8.
FURTHER
EFFORTS
ON
THE
CONTINUUM
HYPOTHESIS
.
210
VII
SETS
AND
MAPS
AS
A
FOUNDATION
FOR
MATHEMATICS
.
215
1.
ORIGINS
OF
DEDEKIND
'
S
PROGRAM
FOR
THE
FOUNDATIONS
OF
ARITHMETIC
.
218
2.
THEORY
OF
SETS,
MAPPINGS,
AND
CHAINS
.
224
VIII
CONTENTS
3.
THROUGH
THE
NATURAL
NUMBERS
TO
PURE
MATHEMATICS
.
232
4.
DEDEKIND
AND
THE
CANTOR-BERNSTEIN
THEOREM
.
239
5.
DEDEKIND
'
S
THEOREM
OF
INFINITY,
AND
EPISTEMOLOGY
.
241
6.
RECEPTION
OF
DEDEKIND
'
S
IDEAS
.
248
VIII
THE
TRANSFINITE
ORDINALS
AND
CANTOR
'
S
MATURE
THEORY
.
257
1.
"
FREE
MATHEMATICS
"
.
259
2.
CANTOR
'
S
NOTION
OF
SET
IN
THE
EARLY
1880S
.
263
3.
THE
TRANSFINITE
(ORDINAL)
NUMBERS
.
267
4.
ORDERED
SETS
.
274
5.
THE
RECEPTION
IN
THE
EARLY
1880S
.
282
6.
CANTOR'
S
THEOREM
.
286
7.
THE
BEITRAGE
ZUR
BEGRIINDUNG
DER
TRANSFINITEN
MENGENLEHRE
.
288
8.
CANTOR
AND
THE
PARADOXES
.
290
PART
THREE:
IN
SEARCH
OF
AN
AXIOM
SYSTEM
.
297
IX
DIFFUSION,
CRISIS,
AND
BIFURCATION:
1890
TO
1914
.
299
1.
SPREADING
SET
THEORY
.
300
2.
THE
COMPLEX
EMERGENCE
OF
THE
PARADOXES
.
306
3.
THE
AXIOM
OF
CHOICE
AND
THE
EARLY
FOUNDATIONAL
DEBATE
.
311
4.
THE
EARLY
WORK
OF
ZERMELO
.
317
5.
RUSSELL
'
S
THEORY
OF
TYPES
.
325
6.
OTHER
DEVELOPMENTS
IN
SET
THEORY
.
333
X
LOGIC
AND
TYPE
THEORY
IN
THE
INTERWAR
PERIOD
.
337
1.
AN
ATMOSPHERE
OF
INSECURITY:
WEYL,
BROUWER,
HILBERT
.
338
2.
DIVERGING
CONCEPTIONS
OF
LOGIC
.
345
3.
THE
ROAD
TO
THE
SIMPLE
THEORY
OF
TYPES
.
348
4.
TYPE
THEORY
AT
ITS
ZENITH
.
353
5.
A
RADICAL
PROPOSAL:
WEYL
AND
SKOLEM
ON
FIRST-ORDER
LOGIC
.
357
XI
CONSOLIDATION
OF
AXIOMATIC
SET
THEORY
.
365
1.
THE
CONTRIBUTIONS
OF
FRAENKEL
.
366
CONTENTS
IX
2.
TOWARD
THE
MODEM
AXIOM
SYSTEM:
VON
NEUMANN
AND
ZERMELO
.
370
3.
THE
SYSTEM
VON
NEUMANN-BEMAYS-GODEL
.
378
4.GDDEL
'
S
RELATIVE
CONSISTENCY
RESULTS
.
382
5.
FIRST-ORDER
AXIOMATIC
SET
THEORY
.
386
6.
A
GLANCE
AHEAD:
MATHEMATICIANS
AND
FOUNDATIONS
AFTER
WORLD
WAR
II
.
388
BIBLIOGRAPHICAL
REFERENCES
.
393
INDEX
OF
ILLUSTRATIONS
.
422
NAME
INDEX
.
423
SUBJECT
INDEX
.
430 |
| any_adam_object | 1 |
| author | Ferreirós Domínguez, José |
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| dewey-full | 511.3/22/09 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/22/09 |
| dewey-search | 511.3/22/09 |
| dewey-sort | 3511.3 222 19 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie |
| era | Geschichte 1850-1940 gnd |
| era_facet | Geschichte 1850-1940 |
| format | Book |
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| id | DE-604.BV012555997 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T03:47:20Z |
| institution | BVB |
| isbn | 3764357495 0817657495 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008525637 |
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| physical | XXI, 440 S. Ill., graph. Darst. |
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| publisher | Birkhäuser |
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| series | Science networks |
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| spelling | Ferreirós Domínguez, José Verfasser (DE-588)121021351 aut Labyrinth of thought a history of set theory and its role in modern mathematics José Ferreirós Basel [u.a.] Birkhäuser 1999 XXI, 440 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Science networks 23 Geschichte 1850-1940 gnd rswk-swf Ensembles, Théorie des - Histoire Teoria dos conjuntos (história) larpcal Verzamelingen (wiskunde) gtt Geschichte Set theory History Geschichte (DE-588)4020517-4 gnd rswk-swf Mengenlehre (DE-588)4074715-3 gnd rswk-swf Mengenlehre (DE-588)4074715-3 s Geschichte (DE-588)4020517-4 s DE-604 Geschichte 1850-1940 z Science networks 23 (DE-604)BV002495563 23 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008525637&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ferreirós Domínguez, José Labyrinth of thought a history of set theory and its role in modern mathematics Science networks Ensembles, Théorie des - Histoire Teoria dos conjuntos (história) larpcal Verzamelingen (wiskunde) gtt Geschichte Set theory History Geschichte (DE-588)4020517-4 gnd Mengenlehre (DE-588)4074715-3 gnd |
| subject_GND | (DE-588)4020517-4 (DE-588)4074715-3 |
| title | Labyrinth of thought a history of set theory and its role in modern mathematics |
| title_auth | Labyrinth of thought a history of set theory and its role in modern mathematics |
| title_exact_search | Labyrinth of thought a history of set theory and its role in modern mathematics |
| title_full | Labyrinth of thought a history of set theory and its role in modern mathematics José Ferreirós |
| title_fullStr | Labyrinth of thought a history of set theory and its role in modern mathematics José Ferreirós |
| title_full_unstemmed | Labyrinth of thought a history of set theory and its role in modern mathematics José Ferreirós |
| title_short | Labyrinth of thought |
| title_sort | labyrinth of thought a history of set theory and its role in modern mathematics |
| title_sub | a history of set theory and its role in modern mathematics |
| topic | Ensembles, Théorie des - Histoire Teoria dos conjuntos (história) larpcal Verzamelingen (wiskunde) gtt Geschichte Set theory History Geschichte (DE-588)4020517-4 gnd Mengenlehre (DE-588)4074715-3 gnd |
| topic_facet | Ensembles, Théorie des - Histoire Teoria dos conjuntos (história) Verzamelingen (wiskunde) Geschichte Set theory History Mengenlehre |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008525637&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002495563 |
| work_keys_str_mv | AT ferreirosdominguezjose labyrinthofthoughtahistoryofsettheoryanditsroleinmodernmathematics |