Set theory and its philosophy: a critical introduction
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon
2004
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 345 S. |
| ISBN: | 0199269734 0199270414 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | SET THEORY AND ITS PHILOSOPHY A CRITICAL INTRODUCTION MICHAEL POTTER
OXFORD UNIVERSITY PRESS CONTENTS I SETS INTRODUCTION TO PART I 1 LOGIC
1.1 1.2 1.3 1.4 1.5 THE AXIOMATIC METHOD THE BACKGROUND LOGIC SCHEMES
THE CHOICE OF LOGIC DEFINITE DESCRIPTIONS NOTES COLLECTIONS 2.1 2.2 2.3
2.4 2.5 2.6 COLLECTIONS AND FUSIONS MEMBERSHIP RUSSELL S PARADOX IS IT A
PARADOX? INDEFINITE EXTENSIBILITY COLLECTIONS NOTES THE 3.1 3.2 3.3 3.4
3.5 3.6 3.7 3.8 HIERARCHY TWO STRATEGIES CONSTRUCTION METAPHYSICAL
DEPENDENCE LEVELS AND HISTORIES THE AXIOM SCHEME OF SEPARATION THE
THEORY OF LEVELS SETS PURITY 6 11 13 16 18 20 21 21 23 25 26 27 30 32 34
34 36 38 40 42 43 47 50 51 1 53 1 55 1 55 1 57 1 58 1 60 1 61 I 63 1 65
1 67 1 68 1 72 1 75 I I 7.2 COMPLETENESS I 7.3 THE REAL LINE 1 7.4
SOUSLIN LINES | 7.5 THE BAIRE LINE | NOTES 1 B 8 REAL NUMBERS *I 8.1
EQUIVALENCE RELATIONS K 8.2 INTEGRAL NUMBERS *K 8.3 RATIONAL NUMBERS *:.
8.4 REAL NUMBERS H| 8.5 THE UNCOUNTABILITY OF THE REI HI 8.6 ALGEBRAIC
REAL NUMBERS H| 8.7 ARCHIMEDEAN ORDERED FIELDS HFE 8.8 NON-STANDARD
ORDERED FIELDS 76 NOTES CONCLUSION TO PART II 79 81 88 88 89 92 95 98
101 103 103 106 108 110 113 114 116 117 117 ILL CARDINALS AND ORDINAK
INTRODUCTION TO PART III SI: CARDINALS I FR . 9.1 DEFINITION OF
CARDINALS . 9.2 THE PARTIAL ORDERING *9.3 FINITE AND INFINITE 9.4 THE
AXIOM OF COUNTABLE CHOI I-NOTCS IC CARDINAL ARITHMETIC TO. 1 FINITE
CARDINALS 10.2 CARDINAL ARITHMETIC INFINITE CARDINALS 9.4 THE POWER OF
THE CONTINUUM WELL-ORDERING ORDINALS TRANSFINITE INDUCTION AND RE
CONTENTS XI 7.2 7.3 7.4 7.5 NOTE: REAL 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8
COMPLETENESS THE REAL LINE SOUSLIN LINES THE BAIRE LINE NUMBERS
EQUIVALENCE RELATIONS INTEGRAL NUMBERS RATIONAL NUMBERS REAL NUMBERS THE
UNCOUNTABILITY OF THE REAL NUMBERS ALGEBRAIC REAL NUMBERS ARCHIMEDEAN
ORDERED FIELDS NON-STANDARD ORDERED FIELDS NOTES CONCLUSION TO PART II
119 121 125 126 128 129 129 130 132 135 136 138 140 144 147 149 HI
CARDINALS AND ORDINALS INTRODUCTION TO PART III 151 153 9 CARDINALS 9.1
9.2 9.3 9.4 NOTES DEFINITION OF CARDINALS THE PARTIAL ORDERING FINITE
AND INFINITE THE AXIOM OF COUNTABLE CHOICE 10 BASIC CARDINAL ARITHMETIC
10.1 FINITE CARDINALS 10.2 CARDINAL ARITHMETIC 10.3 INFINITE CARDINALS
10.4 THE POWER OF THE CONTINUUM NOTES 11 ORDINALS 11.1 WELL-ORDERING
11.2 ORDINALS 11.3 TRANSFINITE INDUCTION AND RECURSION 155 155 157 159
161 165 167 167 168 170 172 174 175 175 179 182 XII CONTENTS 11.4
CARDINALITY 184 11.5 RANK 186 NOTES 189 12 ORDINAL ARITHMETIC 191 12.1
NORMAL FUNCTIONS 191 12.2 ORDINAL ADDITION 192 12.3 ORDINAL
MULTIPLICATION 196 12.4 ORDINAL EXPONENTIATION 199 12.5 NORMAL FORM 202
NOTES 204 CONCLUSION TO PART III 205 IV FURTHER AXIOMS 207 INTRODUCTION
TO PART IV 209 13 ORDERS OF INFINITY 211 13.1 GOODSTEIN S THEOREM 212
13.2 THE AXIOM OF ORDINALS 218 13.3 REFLECTION 221 13.4 REPLACEMENT 225
13.5 LIMITATION OF SIZE 227 13.6 BACK TO DEPENDENCY? 230 13.7 HIGHER
STILL 231 13.8 SPEED-UP THEOREMS 234 NOTES 236 14 THE AXIOM OF CHOICE
238 14.1 THE AXIOM OF COUNTABLE DEPENDENT CHOICE 238 14.2 SKOLEM S
PARADOX AGAIN 240 14.3 THE AXIOM OF CHOICE 242 14.4 THE WELL-ORDERING
PRINCIPLE 243 14.5 MAXIMAL PRINCIPLES 245 14.6 REGRESSIVE ARGUMENTS 250
14.7 THE AXIOM OF CONSTRUCTIBILITY 252 14.8 INTUITIVE ARGUMENTS 256
NOTES 259 15 FURTHER CARDINAL ARITHMETIC 261 15.1 ALEPHS 261 CONTENTS
XIII 15.2 THE ARITHMETIC OF ALEPHS 15.3 COUNTING WELL-ORDERABLE SETS
15.4 CARDINAL ARITHMETIC AND THE AXIOM OF CHOICE 15.5 THE CONTINUUM
HYPOTHESIS 15.6 IS THE CONTINUUM HYPOTHESIS DECIDABLE? 15.7 THE AXIOM OF
DETERMINACY 15.8 THE GENERALIZED CONTINUUM HYPOTHESIS NOTES 262 263 266
268 270 275 280 283 CONCLUSION TO PART IV 284 APPENDICES A TRADITIONAL
AXIOMATIZATIONS A. 1 ZERMELO S AXIOMS A.2 CARDINALS AND ORDINALS A. 3
REPLACEMENT NOTES 289 291 291 292 296 298 B CLASSES C B.I B.2 B.3 B.4
B.5 B.6 B.7 SETS VIRTUAL CLASSES CLASSES AS NEW ENTITIES CLASSES AND
QUANTIFICATION CLASSES QUANTIFIED IMPREDICATIVE CLASSES IMPREDICATIVITY
USING CLASSES TO ENRICH THE ORIGINAL THEORY AND CLASSES C. 1 ADDING
CLASSES TO SET THEORY C.2 THE DIFFERENCE BETWEEN SETS AND CLASSES C.3
THE METALINGUISTIC PERSPECTIVE NOTES 299 300 302 303 306 307 308 310 312
312 313 315 316 REFERENCES LIST OF SYMBOLS INDEX OF DEFINITIONS INDEX OF
NAMES 317 329 331 336
|
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| dewey-full | 511.3/22 511.322 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
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| dewey-search | 511.3/22 511.322 |
| dewey-sort | 3511.3 222 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie |
| edition | 1. publ. |
| format | Book |
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| indexdate | 2024-07-09T20:00:49Z |
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| isbn | 0199269734 0199270414 |
| language | English |
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| physical | XIII, 345 S. |
| publishDate | 2004 |
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| publisher | Clarendon |
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| spelling | Potter, Michael D. 1960- Verfasser (DE-588)1089522495 aut Set theory and its philosophy a critical introduction Michael Potter 1. publ. Oxford Clarendon 2004 XIII, 345 S. txt rdacontent n rdamedia nc rdacarrier Ensembles, Théorie des - Philosophie Filosofia da matemática larpcal Philosophie Set theory Philosophy Mathematik (DE-588)4037944-9 gnd rswk-swf Philosophie (DE-588)4045791-6 gnd rswk-swf Mathematik (DE-588)4037944-9 s Philosophie (DE-588)4045791-6 s b DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012920795&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Potter, Michael D. 1960- Set theory and its philosophy a critical introduction Ensembles, Théorie des - Philosophie Filosofia da matemática larpcal Philosophie Set theory Philosophy Mathematik (DE-588)4037944-9 gnd Philosophie (DE-588)4045791-6 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4045791-6 |
| title | Set theory and its philosophy a critical introduction |
| title_auth | Set theory and its philosophy a critical introduction |
| title_exact_search | Set theory and its philosophy a critical introduction |
| title_full | Set theory and its philosophy a critical introduction Michael Potter |
| title_fullStr | Set theory and its philosophy a critical introduction Michael Potter |
| title_full_unstemmed | Set theory and its philosophy a critical introduction Michael Potter |
| title_short | Set theory and its philosophy |
| title_sort | set theory and its philosophy a critical introduction |
| title_sub | a critical introduction |
| topic | Ensembles, Théorie des - Philosophie Filosofia da matemática larpcal Philosophie Set theory Philosophy Mathematik (DE-588)4037944-9 gnd Philosophie (DE-588)4045791-6 gnd |
| topic_facet | Ensembles, Théorie des - Philosophie Filosofia da matemática Philosophie Set theory Philosophy Mathematik |
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