Set theory with a universal set: exploring an untyped universe
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Clarendon Press
1995
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Oxford logic guides
31 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 166 S. |
| ISBN: | 0198514778 |
Internformat
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| 250 | |a 2. ed. | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS
1 Introduction 1
1.1 Annotated definitions 4
1.1.1 Quantifier hierarchies 5
1.1.2 Mainly concerning type theory 6
1.1.3 Other definitions 9
1.1.4 Theories 10
1.2 Some motivations and axioms 11
1.2.1 Sets as predicates in extension 11
1.2.2 Sets as natural kinds 21
1.3 A brief survey 22
1.4 How do theories with V 6 V avoid the paradoxes? 24
1.5 Chronology 25
2 NF and related systems 26
2.1 NF 26
2.1.1 The axiom of counting 30
2.1.2 BofFa s lemma on n formulae, and the auto¬
morphism lemma for set abstracts 33
2.1.3 Miscellaneous combinatorics 35
2.1.4 Well founded sets 40
2.2 Cardinal and ordinal arithmetic 44
2.2.1 Some remarks on inductive definitions 55
2.2.2 Closure properties of small sets 57
2.3 The Kaye Specker equiconsistency lemma 58
2.3.1 NF3 65
2.3.2 NFU 67
2.3.3 Lake s model 72
2.3.4 KF 72
2.4 Subsystems, term models, and prefix classes 83
2.5 The converse consistency problem 89
3 Permutation models 92
3.1 Permutations in NF 96
3.1.1 Inner permutations in NF 97
3.1.2 Outer automorphisms in NF 119
3.2 Applications to other theories 121
x PREFACE TO THE FIRST EDITION
4 Church Oswald models 122
4.1 Oswald s model 122
4.2 Low sets 124
4.2.1 Other definitions of low 125
4.3 P extensions and permutation models 126
4.3.1 P extensions 126
4.3.2 Hereditarily low sets and permutation mod¬
els 127
4.3.3 Permutation models of CO structures 129
4.4 Two applications 130
4.4.1 An elementary example 130
4.4.2 ^ extending models of Zermelo to models of
NFO 132
4.5 Church s model 136
4.6 Mitchell s set theory 139
4.7 Conclusions 140
5 Open problems 143
5.1 Permutation models and quantifier hierarchies 143
5.2 Cardinals and ordinals in NF 144
5.3 KF 144
5.4 Other subsystems 145
5.5 Well founded extensional relations 145
5.6 Term models 146
5.7 Miscellaneous 146
Bibliography 148
Index of definitions 161
Author index 163
General index 164
|
| any_adam_object | 1 |
| author | Forster, T. E. |
| author_facet | Forster, T. E. |
| author_role | aut |
| author_sort | Forster, T. E. |
| author_variant | t e f te tef |
| building | Verbundindex |
| bvnumber | BV010497511 |
| classification_rvk | SK 150 |
| ctrlnum | (OCoLC)246784876 (DE-599)BVBBV010497511 |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV010497511 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:53:29Z |
| institution | BVB |
| isbn | 0198514778 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006994903 |
| oclc_num | 246784876 |
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| physical | X, 166 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Clarendon Press |
| record_format | marc |
| series | Oxford logic guides |
| series2 | Oxford logic guides |
| spelling | Forster, T. E. Verfasser aut Set theory with a universal set exploring an untyped universe T. E. Forster 2. ed. Oxford [u.a.] Clarendon Press 1995 X, 166 S. txt rdacontent n rdamedia nc rdacarrier Oxford logic guides 31 Mengenlehre (DE-588)4074715-3 gnd rswk-swf Mengenlehre (DE-588)4074715-3 s DE-604 Oxford logic guides 31 (DE-604)BV000013997 31 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006994903&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Forster, T. E. Set theory with a universal set exploring an untyped universe Oxford logic guides Mengenlehre (DE-588)4074715-3 gnd |
| subject_GND | (DE-588)4074715-3 |
| title | Set theory with a universal set exploring an untyped universe |
| title_auth | Set theory with a universal set exploring an untyped universe |
| title_exact_search | Set theory with a universal set exploring an untyped universe |
| title_full | Set theory with a universal set exploring an untyped universe T. E. Forster |
| title_fullStr | Set theory with a universal set exploring an untyped universe T. E. Forster |
| title_full_unstemmed | Set theory with a universal set exploring an untyped universe T. E. Forster |
| title_short | Set theory with a universal set |
| title_sort | set theory with a universal set exploring an untyped universe |
| title_sub | exploring an untyped universe |
| topic | Mengenlehre (DE-588)4074715-3 gnd |
| topic_facet | Mengenlehre |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006994903&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT forsterte settheorywithauniversalsetexploringanuntypeduniverse |