Natural dualities for the working algebraist:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1998
|
| Edition: | 1. publ. |
| Series: | Cambridge studies in advanced mathematics
57 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008142300&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | XII, 356 S. |
| ISBN: | 0521454158 |
Staff View
MARC
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| 245 | 1 | 0 | |a Natural dualities for the working algebraist |c David M. Clark and Brian A. Davey |
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| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 1998 | |
| 300 | |a XII, 356 S. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
ix
1.
Dual Equivalences and Where to Find Them
1
1.
Categories
2
2.
Distributive lattices
7
3.
Quasi-varieties
15
4.
Structured topological spaces
20
5.
Predualities
29
2.
Natural Dualities
39
1.
Brute force
39
2.
Duality theorems
41
3.
Taming brute force with near-unanimity
52
4.
Refining duality via
ent
ailment
55
3.
Strong Dualities
62
1.
Full duality and the dual category
63
2.
Strong duality and the role of injectivity
71
3.
Producing strong dualities
79
4.
Examples of Strong Dualities
94
1.
Strong dualities from
primali
ty
and its variants
94
2.
Arithmetical strong dualities
98
3. NU
strong dualities
102
4.
Two-for-one strong dualities
113
5.
Vagrant dualities
116
5.
Sample Applications
124
1.
Compactness of propositional logic
124
2.
Endomorphism monoids and upside down lattices
125
3.
Theory of algebraic and existential closure
129
4.
Examples of algebraic and existential closure
135
5.
Injectives, weak injectives and absolute subretracts
144
6.
Category equivalences
159
6.
What Makes a Duality Useful?
171
1.
Total structures and injectivity
173
2.
Unary structures, coproducts and near-unanimity
177
3.
Better coproducts and logarithmicity
182
4.
Exclusively unary structures and arithmeticity
186
viii Contents
7.
Piggyback Dualities
1.
Multisorted dualities
2.
Piggyback dualities for distributive-lattice-based algebras
3.
Piggyback dualities for varieties of Hey ting algebras
4.
Restricted Priestley dualities
5.
Piggyback dualities for varieties of Ockham algebras
6.
Piggyback dualities for varieties of distributive p-algebras
7.
Completely dualisable quasi-varieties
8.
Endodualisable algebras
8.
Optimal Dualities and Entailment
1.
Test algebras
—
schizophrenia strikes again!
2.
Entailment closure and the topology of failsets
3.
Failsets and optimal dualities
4.
Kleene algebras once again
5.
The structure of failsets
6.
Optimal dualities for varieties of distributive p-algebras
9.
Completeness Theorems for Entailment
1.
The syntax of entailment
2.
Completeness of constructs for entailment
3.
Local entailment
4.
Optimal strong dualities and hom-entailment
5.
An example: the three-element chain
10.
Dualisable Algebras
1.
Dualisability
2.
Near-unanimity as an obstacle to duality
3.
Some applications of the
NU
obstacle theorems
4.
The balanced
subalgebra
method
5.
The ghost element method
6.
The term-closed subset method
7.
Dualisable clones on a two-element set
Appendix A: Algebras
Appendix B: Boolean Spaces
Bibliography
Notation
Index
|
| any_adam_object | 1 |
| author | Clark, David M. 1954- Davey, Brian A. |
| author_GND | (DE-588)110087666 |
| author_facet | Clark, David M. 1954- Davey, Brian A. |
| author_role | aut aut |
| author_sort | Clark, David M. 1954- |
| author_variant | d m c dm dmc b a d ba bad |
| building | Verbundindex |
| bvnumber | BV012033026 |
| classification_rvk | SK 200 |
| ctrlnum | (OCoLC)438994792 (DE-599)BVBBV012033026 |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV012033026 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:23:04Z |
| institution | BVB |
| isbn | 0521454158 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008142300 |
| oclc_num | 438994792 |
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| physical | XII, 356 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spellingShingle | Clark, David M. 1954- Davey, Brian A. Natural dualities for the working algebraist Cambridge studies in advanced mathematics Dualitätstheorie (DE-588)4150801-4 gnd Algebra (DE-588)4001156-2 gnd Dualität (DE-588)4013161-0 gnd |
| subject_GND | (DE-588)4150801-4 (DE-588)4001156-2 (DE-588)4013161-0 |
| title | Natural dualities for the working algebraist |
| title_auth | Natural dualities for the working algebraist |
| title_exact_search | Natural dualities for the working algebraist |
| title_full | Natural dualities for the working algebraist David M. Clark and Brian A. Davey |
| title_fullStr | Natural dualities for the working algebraist David M. Clark and Brian A. Davey |
| title_full_unstemmed | Natural dualities for the working algebraist David M. Clark and Brian A. Davey |
| title_short | Natural dualities for the working algebraist |
| title_sort | natural dualities for the working algebraist |
| topic | Dualitätstheorie (DE-588)4150801-4 gnd Algebra (DE-588)4001156-2 gnd Dualität (DE-588)4013161-0 gnd |
| topic_facet | Dualitätstheorie Algebra Dualität |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008142300&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003678 |
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