Localization and iteration of axiomatic set theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Detroit, MI
Wayne State Univ. Press
1969
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 226 S. |
Staff View
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| 245 | 1 | 0 | |a Localization and iteration of axiomatic set theory |c Arthur H. Kruse |
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Record in the Search Index
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| adam_text | contents
PREFACE 7
INTRODUCTION 9
1. Logical setting 9
2. The axiomatic theory of Chapter I 11
3. Philosophical perspective 19
4. Local mathematics 21
5. The developments in Chapter II 22
6. Iteration of axiomatic set theory 23
7. The metamathematical role of the iteration of
axiomatic set theory 27
CHAPTER I An Axiomatic Set Theory 31
1. The basic predicates 31
2. Axiom Group A 31
3. Axiom Group Bo 33
4. Semiformalization 37
5. Formalization 41
6. Comments on Axiom Group Bo 44
7. Ordering relations and finite classes 53
8. Ordinals 62
9. Axiom B 6 68
10. Axioms SI and S2 71
11. Axioms S3 and S4 84
12. Lower closures 85
13. Upper closures 87
14. Vertical closures 96
15. Local universes 97
16. Axiom Group B 103
5
Contents
17. Comments on Axiom Group B 106
18. Axiom Group C 112
19. Axiom D 118
20. Axiom E 120
21. Amenable classes 123
22. Central formulae 126
CHAPTER II Some Technical Developments 128
1. Preliminaries 128
2. The functions q XiY 129
3. The operations rj(x) and ^(x) 130
4. Neo atoms and neo classes 131
5. The axiom system 21 and the predicates
elto,clsO;6o, =0, ,elt,,cls1,e1, =, 142
6. Objects* 160
7. * Isomorphisms 166
8. The predicates elt;, els;, ei? = j, «, eltn, cls^,
6«. =a 167
9. The independence of axiom D and the non
existence of atoms relative to certain collec¬
tions of axioms 174
10. The predicates elt£, cls£, epn, =pn, and % 176
CHAPTER III Iteration of Axiomatic set theory 180
1. The basic predicates 180
2. The special predicate sp 181
3. Axioms H£, l£, J£, K£, L^, and N{^ for T and A
inC 181
4. Iteration of axiomatic set theory 188
5. The predicates p,q 199
6. The main metatheorems 202
NOTES 208
BIBLIOGRAPHY 213
GENERAL INDEX 217
AXIOM INDEX 223
NOTATION INDEX 225
6
|
| any_adam_object | 1 |
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| discipline | Mathematik |
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| institution | BVB |
| language | English |
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| spelling | Kruse, Arthur H. Verfasser aut Localization and iteration of axiomatic set theory Arthur H. Kruse Detroit, MI Wayne State Univ. Press 1969 226 S. txt rdacontent n rdamedia nc rdacarrier Ensembles, Théorie axiomatique des Ensembles, Théorie axiomatique des ram Axiomatic set theory HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009178323&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kruse, Arthur H. Localization and iteration of axiomatic set theory Ensembles, Théorie axiomatique des Ensembles, Théorie axiomatique des ram Axiomatic set theory |
| title | Localization and iteration of axiomatic set theory |
| title_auth | Localization and iteration of axiomatic set theory |
| title_exact_search | Localization and iteration of axiomatic set theory |
| title_full | Localization and iteration of axiomatic set theory Arthur H. Kruse |
| title_fullStr | Localization and iteration of axiomatic set theory Arthur H. Kruse |
| title_full_unstemmed | Localization and iteration of axiomatic set theory Arthur H. Kruse |
| title_short | Localization and iteration of axiomatic set theory |
| title_sort | localization and iteration of axiomatic set theory |
| topic | Ensembles, Théorie axiomatique des Ensembles, Théorie axiomatique des ram Axiomatic set theory |
| topic_facet | Ensembles, Théorie axiomatique des Axiomatic set theory |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009178323&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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