First order categorical logic: model-theoretical methods in the theory of topoi and related categories
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1977
|
| Schriftenreihe: | Lecture notes in mathematics
611 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 301 S. graph. Darst. |
| ISBN: | 3540084398 0387084398 |
Internformat
MARC
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| 100 | 1 | |a Makkai, Michael |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a First order categorical logic |b model-theoretical methods in the theory of topoi and related categories |c Michael Makkai ; Gonzalo E. Reyes |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1977 | |
| 300 | |a VIII, 301 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 611 | |
| 650 | 4 | |a Catégories (Mathématiques) | |
| 650 | 4 | |a Modèles, Théorie des | |
| 650 | 4 | |a Topos (Mathématiques) | |
| 650 | 4 | |a Categories (Mathematics) | |
| 650 | 4 | |a Model theory | |
| 650 | 4 | |a Toposes | |
| 650 | 0 | 7 | |a Modelltheorie |0 (DE-588)4114617-7 |2 gnd |9 rswk-swf |
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| 650 | 0 | 7 | |a Kategorie |g Mathematik |0 (DE-588)4129930-9 |2 gnd |9 rswk-swf |
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| 689 | 1 | 1 | |a Topos |g Mathematik |0 (DE-588)4185717-3 |D s |
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Datensatz im Suchindex
| _version_ | 1804116419804135424 |
|---|---|
| adam_text | TABLE OF CONTENTS
INTRODUCTION 1
CHAPTER 1 Grothendieck topoi 11
§1 Sites and sheaves 11
§2 The associated sheaf 19
§3 Grothendieck topoi 30
§4 Characterization of Grothendieck topoi:
Giraud s theorem 48
Appendix to Chapter 1. Concepts of local character, examples... 60
CHAPTER 2 Interpretation of the logic L^
in categories 68
§1 The logic L 68
§ 2 Some categorical notions 7 3
§3 The categorical interpretation 78
§4 Expressing categorical notions by formulas:
the first main fact 82
CHAPTER 3 Axioms and rules of inference valid
in categories 96
§1 Some simple rules 96
§2 Stability and distributivity 101
§3 Further categorical notions and their
expression by formulas Ill
§4 Logical categories 121
§ 5 Summary of the two main facts 125
CHAPTER 4 Boolean and Heyting valued models 132
§ 1 Heyting and Boolean valued models 13 2
§ 2 Sheaves over Heyting algebras 136
§3 Boolean homomorphisms 139
CHAPTER 5 Completeness 143
§1 A Boolean-complete formalization of L 144
§2 Completeness of a one-sided system
for coherent logic 159
VIII
CHAPTER 6 Existence theorems on geometric movphisms
of topoi 165
§1 Preliminaries 165
§2 Categorical completeness theorems.. 175
§3 Intuitionistic models 18 0
CHAPTER 7 Conceptual completeness 193
§1 A completeness property of pretopoi 193
§2 Infinitary generalizations; preliminaries 204
§3 Infinitary generalizations 210
§4 Infinitary generalizations (continued) 226
CHAPTER 8 Theories as categories 237
§1 Categories and algebraic logic 237
§2 The categorization of a coherent theory 241
§3 Infinitary generalizations 251
§4 The K-pretopos correlated to a theory 255
CHAPTER 9 Classifying topoi 27 2
§1 Classifying topoi 272
§2 Coherent objects 276
§3 The Zariski topos 286
§4 Appendix. M. Coste s construction of the
classifying topos of a theory 291
§5 Appendix 295
REFERENCES 298
|
| any_adam_object | 1 |
| author | Makkai, Michael Reyes, Gonzalo E. 1937- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra 510 - Mathematics |
| dewey-raw | 512/.55 510/.8 |
| dewey-search | 512/.55 510/.8 |
| dewey-sort | 3512 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV001975346 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:38:13Z |
| institution | BVB |
| isbn | 3540084398 0387084398 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001288390 |
| oclc_num | 721322705 |
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| physical | VIII, 301 S. graph. Darst. |
| publishDate | 1977 |
| publishDateSearch | 1977 |
| publishDateSort | 1977 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Makkai, Michael Verfasser aut First order categorical logic model-theoretical methods in the theory of topoi and related categories Michael Makkai ; Gonzalo E. Reyes Berlin [u.a.] Springer 1977 VIII, 301 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 611 Catégories (Mathématiques) Modèles, Théorie des Topos (Mathématiques) Categories (Mathematics) Model theory Toposes Modelltheorie (DE-588)4114617-7 gnd rswk-swf Topos Mathematik (DE-588)4185717-3 gnd rswk-swf Kategorie Mathematik (DE-588)4129930-9 gnd rswk-swf Kategorie Mathematik (DE-588)4129930-9 s Modelltheorie (DE-588)4114617-7 s DE-604 Topos Mathematik (DE-588)4185717-3 s Reyes, Gonzalo E. 1937- Verfasser (DE-588)108794997 aut Lecture notes in mathematics 611 (DE-604)BV000676446 611 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001288390&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Makkai, Michael Reyes, Gonzalo E. 1937- First order categorical logic model-theoretical methods in the theory of topoi and related categories Lecture notes in mathematics Catégories (Mathématiques) Modèles, Théorie des Topos (Mathématiques) Categories (Mathematics) Model theory Toposes Modelltheorie (DE-588)4114617-7 gnd Topos Mathematik (DE-588)4185717-3 gnd Kategorie Mathematik (DE-588)4129930-9 gnd |
| subject_GND | (DE-588)4114617-7 (DE-588)4185717-3 (DE-588)4129930-9 |
| title | First order categorical logic model-theoretical methods in the theory of topoi and related categories |
| title_auth | First order categorical logic model-theoretical methods in the theory of topoi and related categories |
| title_exact_search | First order categorical logic model-theoretical methods in the theory of topoi and related categories |
| title_full | First order categorical logic model-theoretical methods in the theory of topoi and related categories Michael Makkai ; Gonzalo E. Reyes |
| title_fullStr | First order categorical logic model-theoretical methods in the theory of topoi and related categories Michael Makkai ; Gonzalo E. Reyes |
| title_full_unstemmed | First order categorical logic model-theoretical methods in the theory of topoi and related categories Michael Makkai ; Gonzalo E. Reyes |
| title_short | First order categorical logic |
| title_sort | first order categorical logic model theoretical methods in the theory of topoi and related categories |
| title_sub | model-theoretical methods in the theory of topoi and related categories |
| topic | Catégories (Mathématiques) Modèles, Théorie des Topos (Mathématiques) Categories (Mathematics) Model theory Toposes Modelltheorie (DE-588)4114617-7 gnd Topos Mathematik (DE-588)4185717-3 gnd Kategorie Mathematik (DE-588)4129930-9 gnd |
| topic_facet | Catégories (Mathématiques) Modèles, Théorie des Topos (Mathématiques) Categories (Mathematics) Model theory Toposes Modelltheorie Topos Mathematik Kategorie Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001288390&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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