Constructible sets with applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam
North Holland Publ. Co. [u.a.]
1969
|
| Series: | Studies in logic and the foundations of mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 269 S. |
Staff View
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| 100 | 1 | |a Mostowski, Andrzej |d 1913-1975 |e Verfasser |0 (DE-588)118584510 |4 aut | |
| 245 | 1 | 0 | |a Constructible sets with applications |c A. Mostowski |
| 264 | 1 | |a Amsterdam |b North Holland Publ. Co. [u.a.] |c 1969 | |
| 300 | |a IX, 269 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Studies in logic and the foundations of mathematics | |
| 650 | 4 | |a Ensembles constructibles | |
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| 650 | 4 | |a Axiomatic set theory | |
| 650 | 4 | |a Constructibility (Set theory) | |
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Record in the Search Index
| _version_ | 1804116376476975104 |
|---|---|
| adam_text | CONTENTS
Page
Chapter I. Axioms and auxiliary notions
1. Set theory ZF of Zermelo Fraenkel I
2. The meta theory of classes 2
3. Definitions by transfinite induction. Ranks 8
4. Models, satisfaction 11
5. Derived semantical notions; the Skolem Lowenheim theorem 17
6. The contraction lemma 20
Chapter II. General principles of construction
1. Sufficient conditions for a class to be a model 22
2. The reflection theorem 23
3. Predicatively closed classes 27
4. The fundamental operations 29
Chapter III. Constructible sets
1. Enumeration 36
2. Constructible sets 39
3. Properties of constructible sets 40
4. Constructibility of ordinals 44
5. Models containing with each element its mappings into ordinals .... 46
6. Examples of functions satisfying (B.0) (B.6) 48
7. Sets constructible in a class 48
Chapter IV. Functors and their definability
1. Strongly definable functors 51
2. Properties of strongly definable functors and relations 53
3. Examples of strongly definable functors 55
4. Definitions by transfinite induction 60
5. Why is all that necessary? 65
Chapter V. Constructible sets as values of a functor
1. Uniformly definable functions 69
2. Examples of uniformly definable functions 73
3. Uniform definability of the function C^(a) 76
4. A generalization 81
5. Further properties of constructible sets 82
vJiJ CONTENTS
Page
Chapter VI. Cn,AJji) as a model
1. The reflection theorem again 85
2. Satisfiability of the power set axiom and of the axiom of substitution . 88
3. Existence of models 93
4. Minimal models 96
Chapter VII. Consistency of the axiom of choice and of the continuum
hypothesis
1. Axiom of choice 99
2. Auxiliary functors 102
3. Formulation of the generalized continuum hypothesis 105
4. A sufficient condition for the validity of GCH 107
5. Construction of models in which the continuum hypothesis is valid . . . 108
6. Definability of the contracting function 110
7. A refinement of the Skolem Lowenheim theorem 112
8. Consistency of GCH 115
9. Axioms of constructibility. Final remarks 118
Chapter VIII. Reduction of models
1. A reflection lemma 120
2. The validity of the power set axiom 124
Chapter IX. Generic points and forcing; general theory
1. Auxiliary topological notions . . . . , 128
2. Valuations 130
3. The forcing relation 132
4. A special valuation 134
5. Application of forcing to constructions of models 135
Chapter X. Polynomials
1. Polynomials 141
2. Reduction of Condition IV 145
3. Reduction of Condition V 147
Chapter XI. Explicit construction of polynomials for functions 5mIn, Ba, Bz
1. The partial ordering 0 153
2. Auxiliary polynomials 155
3. Expressing S ? and j f as polynomials of fB:(a,/S) and ,/B|(a,/S) . . 157
4. Generalization to the cases B = Bz and B = B 162
5. Final reduction of Conditions IV and V ? . . 164
6. Appendix: list of the polynomials pj,j 12 168
CONTENTS IX
Page
Chapter XII. Examples of models and of independence proofs
1. Examples of topological spaces 169
2. Examples of mappings p * a(p) 172
3. Proof of Condition VIII for sequences of the first and the second category 173
4. Examples of models 181
5. A theorem on generic points 184
6. Independence of the strong axiom of constructibility 187
Chapter XIII. The continuum hypothesis
1. Auxiliary notions concerning cardinals 190
2. The Souslin coefficient 192
3. The Souslin coefficient of product spaces 195
4. Relative cardinals, relative cofinality and relative Souslin coefficients . 199
5. Determination of the relative Souslin coefficient 204
6. Absoluteness of cardinals and of the cofinality index 206
7. The function exp of a model 212
8. The independence of the continuum hypothesis 219
Chapter XIV. Independence of the axiom of choice
1. Action of homeomorphisms onto sets CSa(p)) 223
2. Homeomorphisms and forcing 227
3. Invariance properties 229
4. Independence of the axiom of choice 229
5. The ordering of P(P(o))) 234
6. The existence of maximal ideals in P(a ) 237
7. Cofinality of co, 241
Chapter XV. Problems of definability
1. Definable relations between ordinals 248
2. Non definability of the well orderings of P( x ) 249
3. Definable well ordered subsets of P(oj) 251
Appendix 255
Bibliography 258
List of important symbols 260
Author index 266
Subject index 267
|
| any_adam_object | 1 |
| author | Mostowski, Andrzej 1913-1975 |
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| callnumber-first | B - Philosophy, Psychology, Religion |
| callnumber-label | BC135 |
| callnumber-raw | BC135 QA9 |
| callnumber-search | BC135 QA9 |
| callnumber-sort | BC 3135 |
| callnumber-subject | BC - Logic |
| classification_rvk | CC 2600 SK 130 SK 150 |
| ctrlnum | (OCoLC)21765 (DE-599)BVBBV001936498 |
| dewey-full | 512/.817 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.817 |
| dewey-search | 512/.817 |
| dewey-sort | 3512 3817 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:37:32Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001262173 |
| oclc_num | 21765 |
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| physical | IX, 269 S. |
| publishDate | 1969 |
| publishDateSearch | 1969 |
| publishDateSort | 1969 |
| publisher | North Holland Publ. Co. [u.a.] |
| record_format | marc |
| series2 | Studies in logic and the foundations of mathematics |
| spelling | Mostowski, Andrzej 1913-1975 Verfasser (DE-588)118584510 aut Constructible sets with applications A. Mostowski Amsterdam North Holland Publ. Co. [u.a.] 1969 IX, 269 S. txt rdacontent n rdamedia nc rdacarrier Studies in logic and the foundations of mathematics Ensembles constructibles Logique symbolique et mathématique Axiomatic set theory Constructibility (Set theory) Model theory Mengenlehre (DE-588)4074715-3 gnd rswk-swf Mengenlehre (DE-588)4074715-3 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001262173&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mostowski, Andrzej 1913-1975 Constructible sets with applications Ensembles constructibles Logique symbolique et mathématique Axiomatic set theory Constructibility (Set theory) Model theory Mengenlehre (DE-588)4074715-3 gnd |
| subject_GND | (DE-588)4074715-3 |
| title | Constructible sets with applications |
| title_auth | Constructible sets with applications |
| title_exact_search | Constructible sets with applications |
| title_full | Constructible sets with applications A. Mostowski |
| title_fullStr | Constructible sets with applications A. Mostowski |
| title_full_unstemmed | Constructible sets with applications A. Mostowski |
| title_short | Constructible sets with applications |
| title_sort | constructible sets with applications |
| topic | Ensembles constructibles Logique symbolique et mathématique Axiomatic set theory Constructibility (Set theory) Model theory Mengenlehre (DE-588)4074715-3 gnd |
| topic_facet | Ensembles constructibles Logique symbolique et mathématique Axiomatic set theory Constructibility (Set theory) Model theory Mengenlehre |
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