Toposes and local set theories: an introduction
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon Press
1988
|
| Series: | Oxford logic guides
14 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 267 S. graph. Darst. |
| ISBN: | 0198532741 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
1. Elements of category theory l
Categories 1
Some basic category theoretic notions 5
Limits and colimits 11
Existence of limits and colimits 16
Functors 18
Natural transformations and functor categories 21
Completeness of functor categories 26
Equivalence of categories 28
Adjunctions 30
Units and counits of adjunctions 32
Freedom and cofreedom 35
Uniqueness of adjoints 38
Preservation of limits and colimits 39
Cartesian closed categories 42
Reflective subcategories 45
Galois connections 46
2. Introducing toposes 49
Subobjects and subobject classifiers 49
Power objects: the concept of topos 58
Setc as a topos 60
Geometric morphisms 65
3. Local set theories 68
Local languages and local set theories 68
Logic in a local set theory 73
Set theory in a local language 83
The category of sets determined by a local set theory 85
Interpreting a local language in a topos: the soundness theorem 91
The completeness theorem 103
The equivalence theorem 105
Translations and logical functors 113
Adjoining indeterminates 115
Introduction of function values 117
4. Fundamental properties of toposes 120
Some fundamental properties of toposes 120
The structure of Q and Sub(/1) in a topos 127
Slicing a topos 131
Coproducts in a topos 136
xii Contents
Syntactic properties of local set theories versus essentially categorical
properties of toposes 141
Full theories 150
Beth Kripke Joyal semantics 155
5. From logic to sheaves 162
Truth sets, modalities, and universal closure operations 162
Sheaves 171
The sheafification functor 180
Modalized toposes 189
Modal operators and sheaves in Set0 1 194
Sheaves over locales and topological spaces 199
6. Locale valued sets 202
Locale valued sets 202
The topos of sheaves on a topological space 209
Decidable, subconstant, and fuzzy sets 210
Boolean extensions as toposes 215
7. Natural numbers and real numbers 220
Natural numbers in local set theories 220
Real numbers in local set theories 226
The free topos 233
8. Epilogue: the wider significance of topos theory 235
From set theory to topos theory 235
Some analogies with the theory of relativity 239
The negation of constancy 242
Appendix: Geometric theories and classifying toposes 246
Historical and bibliographical notes 255
References 258
Index of symbols 261
Index of terms 264
|
| any_adam_object | 1 |
| author | Bell, John L. 1945- |
| author_GND | (DE-588)128411570 |
| author_facet | Bell, John L. 1945- |
| author_role | aut |
| author_sort | Bell, John L. 1945- |
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| building | Verbundindex |
| bvnumber | BV001853805 |
| callnumber-first | Q - Science |
| callnumber-label | QA169 |
| callnumber-raw | QA169.B45 1988 |
| callnumber-search | QA169.B45 1988 |
| callnumber-sort | QA 3169 B45 41988 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 150 SK 155 SK 320 |
| classification_tum | MAT 040f |
| ctrlnum | (OCoLC)243199779 (DE-599)BVBBV001853805 |
| dewey-full | 511.32 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.32 |
| dewey-search | 511.32 |
| dewey-sort | 3511.32 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| institution | BVB |
| isbn | 0198532741 |
| language | English |
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| physical | XII, 267 S. graph. Darst. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Clarendon Press |
| record_format | marc |
| series | Oxford logic guides |
| series2 | Oxford logic guides |
| spelling | Bell, John L. 1945- Verfasser (DE-588)128411570 aut Toposes and local set theories an introduction J. L. Bell Oxford Clarendon Press 1988 XII, 267 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford logic guides 14 Toposes Set theory Logic, Symbolic and mathematical Topos Mathematik (DE-588)4185717-3 gnd rswk-swf Topos (DE-588)4127974-8 gnd rswk-swf Logik (DE-588)4036202-4 gnd rswk-swf Mengenlehre (DE-588)4074715-3 gnd rswk-swf Topos (DE-588)4127974-8 s Logik (DE-588)4036202-4 s DE-604 Topos Mathematik (DE-588)4185717-3 s Mengenlehre (DE-588)4074715-3 s Oxford logic guides 14 (DE-604)BV000013997 14 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001227562&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bell, John L. 1945- Toposes and local set theories an introduction Oxford logic guides Toposes Set theory Logic, Symbolic and mathematical Topos Mathematik (DE-588)4185717-3 gnd Topos (DE-588)4127974-8 gnd Logik (DE-588)4036202-4 gnd Mengenlehre (DE-588)4074715-3 gnd |
| subject_GND | (DE-588)4185717-3 (DE-588)4127974-8 (DE-588)4036202-4 (DE-588)4074715-3 |
| title | Toposes and local set theories an introduction |
| title_auth | Toposes and local set theories an introduction |
| title_exact_search | Toposes and local set theories an introduction |
| title_full | Toposes and local set theories an introduction J. L. Bell |
| title_fullStr | Toposes and local set theories an introduction J. L. Bell |
| title_full_unstemmed | Toposes and local set theories an introduction J. L. Bell |
| title_short | Toposes and local set theories |
| title_sort | toposes and local set theories an introduction |
| title_sub | an introduction |
| topic | Toposes Set theory Logic, Symbolic and mathematical Topos Mathematik (DE-588)4185717-3 gnd Topos (DE-588)4127974-8 gnd Logik (DE-588)4036202-4 gnd Mengenlehre (DE-588)4074715-3 gnd |
| topic_facet | Toposes Set theory Logic, Symbolic and mathematical Topos Mathematik Topos Logik Mengenlehre |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001227562&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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