Topoi: the categorial analysis of logic
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
North Holland
1984
|
| Edition: | Rev. ed. |
| Series: | Studies in logic and the foundations of mathematics
98 |
| Subjects: | |
| Online Access: | Volltext Inhaltsverzeichnis |
| Physical Description: | XVI, 551 S. |
| ISBN: | 0444867112 |
Staff View
MARC
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| 245 | 1 | 0 | |a Topoi |b the categorial analysis of logic |c Robert Goldblatt |
| 250 | |a Rev. ed. | ||
| 264 | 1 | |a Amsterdam [u.a.] |b North Holland |c 1984 | |
| 300 | |a XVI, 551 S. | ||
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Record in the Search Index
| _version_ | 1804114623309283328 |
|---|---|
| adam_text | Preface ix
Preface to Second Edition xiv
Prospectus 1
Chapter 1.
Mathematics = Set Theory? 6
1. Set theory 6
2. Foundations of mathematics . 13
3. Mathematics as set theory . . 14
Chapter 2.
What Categories Are 17
1. Functions are sets? 17
2. Composition of functions ... 20
3. Categories: first examples ... 23
4. The pathology of abstraction . . 25
5. Basic examples 26
Chapter 3.
Arrows Instead of Epsilon 37
1. Monic arrows 37
2. Epic arrows 39
3. Iso arrows 39
4. Isomorphic objects 41
5. Initial objects 43
6. Terminal objects 44
7. Duality 45
8. Products 46
9. Co products 54
10. Equalisers 56
11. Limits and co limits 58
12. Co equalisers 60
13. The pullback 63
14. Pushouts 68
15. Completeness 69
16. Exponentiation 70
Chapter 4.
Introducing Topoi 75
1. Subobjects 75
2. Classifying subobjects 79
3. Definition of topos 84
4. First examples 85
5. Bundles and sheaves 88
6. Monoid actions 100
7. Power objects 103
8. O and comprehension 107
Chapter 5.
Topos Structure: First Steps 109
1. Monies equalise 109
2. Images of arrows 110
3. Fundamental facts 114
4. Extensionality and bivalence . . 115
5. Monies and epics by elements . 123
Chapter 6.
Logic Classically Conceived 125
1. Motivating topos logic .... 125
2. Propositions and truth values . 126
3. The propositional calculus ... 129
4. Boolean algebra 133
5. Algebraic semantics 135
6. Truth functions as arrows ... 136
7. ^ semantics 140
Chapter 7.
Algebra of Subobjects 146
1. Complement, intersection, union 146
2. Sub(d) as a lattice 151
3. Boolean topoi 156
4. Internal vs. external 159
5. Implication and its implications 162
6. Filling two gaps 166
7. Extensionality revisited .... 168
Chapter 8.
Intuitionism and its Logic 173
1. Construct!vist philosophy ... 173
2. Heyting s calculus 177
3. Heyting algebras 178
4. Kripke semantics 187
Chapter 9.
Functors 194
1. The concept of functor .... 194
2. Natural transformations .... 198
3. Functor categories 202
Chapter 10.
Set Concepts and Validity 211
1. Set concepts 211
2. Heyting algebras in P 213
3. The subobject classifier in Set . 215
4. The truth arrows 221
5. Validity 223
6. Applications 227
Chapter 11.
Elementary Truth 230
1. The idea of a first order lan¬
guage 230
2. Formal language and seman¬
tics 234
3. Axiomatics 237
4. Models in a topos 238
5. Substitution and soundness . . 249
6. Kripke models 256
7. Completeness 264
8. Existence and free logic . . . 266
9. Heyting valued sets 274
10. High order logic 286
Chapter 12.
Categorial Set Theory 289
1. Axioms of choice 290
2. Natural numbers objects . . . 301
3. Formal set theory 305
4. Transitive sets 313
5. Set objects 320
6. Equivalence of models .... 328
Chapter 13.
Arithmetic 332
1. Topoi as foundations 332
2. Primitive recursion 335
3. Peano postulates 347
Chapter 14.
Local Truth 359
1. Stacks and sheaves 359
2. Classifying stacks and sheaves . 368
3. GrothendieCk topoi 374
4. Elementary sites 378
5. Geometric modality 381
6. Kripke Joyal semantics .... 386
7. Sheaves as complete fl sets . . 388
8. Number systems as sheaves . . 413
Chapter 15.
Adjointness and Quantifiers 438
1. Adjunctions 438
2. Some adjoint situations .... 442
3. The fundamental theorem . . . 449
4. Quantifiers . 453
Chapter 16.
Logical Geometry 458
1. Preservation and reflection . . . 459
2. Geometric morphisms 463
3. Internal logic 483
4. Geometric logic 493
5. Theories as sites 504
References 521
Catalogue of Notation . . 531
Index of Definitions .... 541
|
| any_adam_object | 1 |
| author | Goldblatt, Robert 1949- |
| author_GND | (DE-588)1025661435 |
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| dewey-full | 512.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.55 |
| dewey-search | 512.55 |
| dewey-sort | 3512.55 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Rev. ed. |
| format | Book |
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| id | DE-604.BV000163896 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:09:40Z |
| institution | BVB |
| isbn | 0444867112 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000092971 |
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| physical | XVI, 551 S. |
| psigel | digit |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | North Holland |
| record_format | marc |
| series | Studies in logic and the foundations of mathematics |
| series2 | Studies in logic and the foundations of mathematics |
| spelling | Goldblatt, Robert 1949- Verfasser (DE-588)1025661435 aut Topoi the categorial analysis of logic Robert Goldblatt Rev. ed. Amsterdam [u.a.] North Holland 1984 XVI, 551 S. txt rdacontent n rdamedia nc rdacarrier Studies in logic and the foundations of mathematics 98 Topos (mathématiques) ram Mengenlehre (DE-588)4074715-3 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 gnd rswk-swf 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 Kategorientheorie (DE-588)4120552-2 gnd rswk-swf Kategorie Mathematik (DE-588)4129930-9 gnd rswk-swf Kategorie Mathematik (DE-588)4129930-9 s Mathematische Logik (DE-588)4037951-6 s DE-604 Topos Mathematik (DE-588)4185717-3 s Topos (DE-588)4127974-8 s Kategorientheorie (DE-588)4120552-2 s Logik (DE-588)4036202-4 s 1\p DE-604 Mengenlehre (DE-588)4074715-3 s Studies in logic and the foundations of mathematics 98 (DE-604)BV000893472 98 http://digital.library.cornell.edu/cgi/t/text/text-idx?c=math;idno=gold010 kostenfrei Volltext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000092971&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Goldblatt, Robert 1949- Topoi the categorial analysis of logic Studies in logic and the foundations of mathematics Topos (mathématiques) ram Mengenlehre (DE-588)4074715-3 gnd Mathematische Logik (DE-588)4037951-6 gnd Topos Mathematik (DE-588)4185717-3 gnd Topos (DE-588)4127974-8 gnd Logik (DE-588)4036202-4 gnd Kategorientheorie (DE-588)4120552-2 gnd Kategorie Mathematik (DE-588)4129930-9 gnd |
| subject_GND | (DE-588)4074715-3 (DE-588)4037951-6 (DE-588)4185717-3 (DE-588)4127974-8 (DE-588)4036202-4 (DE-588)4120552-2 (DE-588)4129930-9 |
| title | Topoi the categorial analysis of logic |
| title_auth | Topoi the categorial analysis of logic |
| title_exact_search | Topoi the categorial analysis of logic |
| title_full | Topoi the categorial analysis of logic Robert Goldblatt |
| title_fullStr | Topoi the categorial analysis of logic Robert Goldblatt |
| title_full_unstemmed | Topoi the categorial analysis of logic Robert Goldblatt |
| title_short | Topoi |
| title_sort | topoi the categorial analysis of logic |
| title_sub | the categorial analysis of logic |
| topic | Topos (mathématiques) ram Mengenlehre (DE-588)4074715-3 gnd Mathematische Logik (DE-588)4037951-6 gnd Topos Mathematik (DE-588)4185717-3 gnd Topos (DE-588)4127974-8 gnd Logik (DE-588)4036202-4 gnd Kategorientheorie (DE-588)4120552-2 gnd Kategorie Mathematik (DE-588)4129930-9 gnd |
| topic_facet | Topos (mathématiques) Mengenlehre Mathematische Logik Topos Mathematik Topos Logik Kategorientheorie Kategorie Mathematik |
| url | http://digital.library.cornell.edu/cgi/t/text/text-idx?c=math;idno=gold010 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000092971&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000893472 |
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