The classification of countable homogeneous directed graphs and countable homogeneous n-tournaments:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
1998
|
| Schriftenreihe: | American Mathematical Society: Memoirs of the American Mathematical Society
621 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008067207&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Volume 131, Number 621 (first of 4 numbers) |
| Umfang: | XIII, 161 S. graph. Darst. |
| ISBN: | 0821808362 |
Internformat
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| 100 | 1 | |a Cherlin, Gregory L. |d 1948- |e Verfasser |0 (DE-588)172031974 |4 aut | |
| 245 | 1 | 0 | |a The classification of countable homogeneous directed graphs and countable homogeneous n-tournaments |c Gregory L. Cherlin |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1998 | |
| 300 | |a XIII, 161 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a American Mathematical Society: Memoirs of the American Mathematical Society |v 621 | |
| 500 | |a Volume 131, Number 621 (first of 4 numbers) | ||
| 650 | 7 | |a Permutatiegroepen |2 gtt | |
| 650 | 7 | |a Teoria dos grafos |2 larpcal | |
| 650 | 4 | |a Directed graphs | |
| 650 | 4 | |a Model theory | |
| 650 | 4 | |a Permutation groups | |
| 650 | 4 | |a Ramsey theory | |
| 650 | 4 | |a Tournaments (Graph theory) | |
| 650 | 0 | 7 | |a Gerichteter Graph |0 (DE-588)4156815-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Turnier |g Mathematik |0 (DE-588)4473306-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Modelltheorie |0 (DE-588)4114617-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Permutationsgruppe |0 (DE-588)4173833-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Ramsey-Theorie |0 (DE-588)4212682-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Turnier |g Mathematik |0 (DE-588)4473306-9 |D s |
| 689 | 0 | 1 | |a Gerichteter Graph |0 (DE-588)4156815-1 |D s |
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| 689 | 0 | 4 | |a Permutationsgruppe |0 (DE-588)4173833-0 |D s |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 001z 2001 B 990-621/624 |
|---|---|
| DE-BY-TUM_katkey | 1565309 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040020379642 |
| _version_ | 1821933358760853504 |
| adam_text | Contents
Introduction xi
Chapter 1. Results and Open Problems 1
1.1. Homogeneous structures. 1
1.2. A survey of work on homogeneous structures. 3
1.3. Amalgamation classes. 6
1.4. Languages, strong amalgamation, generification,
and Ramsey s theorem 9
1.5. Classification theorems. 12
1.6. Open problems. 13
Chapter 2. Homogeneous 2 tournaments 17
2.1. A catalog. 17
2.2. Restricted homogeneous 2 tournaments. 21
2.3. Sources and sinks 26
2.4. Constrained 2 tournaments 28
2.5. Unconstrained 2 tournaments 33
Chapter 3. Homogeneous n tournaments 38
3.1. Introduction 38
3.2. Hypercritical and small 3 tournaments 39
3.3. The critical case 40
3.4. Two embedding lemmas. 45
3.5. Polarized n tournaments 47
3.6. Embedding polarized 3 tournaments 48
3.7. Some special cases 49
3.8. The general case 51
Chapter 4. Homogeneous symmetric graphs 53
4.1. The theorem of Lachlan and Woodrow 53
4.2. The main ingredients 55
4.3. Structure of the proof 56
4.4. Steps 7, 5, 8. Proof of the Main Theorems 56
4.5. Step 1, Proposition 10: adding K(2) 58
4.6. Step 1, Proposition 11: the operation H+ 60
4.7. Step 1, Propositions 12 and 13: realization of 1 types 62
4.8. Step 2. Theorem 4.8: a, b, K 66
4.9. Step 6. Theorem 4.9.n: extending direct sums 66
4.10. Step 3. Theorem 4.6 66
4.11. Step 4. Theorem 4.7 67
ix
x CONTENTS
Chapter 5. Homogeneous directed graphs omitting 1^ 74
5.1. A catalog of homogeneous directed graphs 74
5.2. The graph V(3) 76
5.3. The theorem 77
5.4. The major steps in the proof 79
5.5. Proof of the Main Theorem, Part 1 80
5.6. Proof of the Main Theorem, part 2, n 2 82
5.7. Case 2.1 of the Main Theorem 83
5.8. Propositions 14 and 15 84
Chapter 6. Propositions 16 to 20 and MT 2.2 91
6.1. Proposition 16: simple configurations 91
6.2. Proposition 17: induction on n 93
6.3. Proposition 18: extending /„ 95
6.4. Proposition 19: (py, y ) 96
6.5. Proposition 20: (pj/,yx) 97
6.6. Toward MT 2.2 99
6.7. Lemma 6.3 101
6.8. Lemma 6.4 104
6.9. Lemma 6.5 110
6.10. Lemma 6.6 117
Chapter 7. Homogeneous directed graphs embedding / *, 119
7.1. The classification theorem 119
7.2. The main ingredients 121
7.3. Structure of the proof 122
7.4. Steps 4, 6, 7. The Main Theorem 123
7.5. Step 1. Proposition 24: P3 125
7.6. Step 1, Proposition 25: adding L(2) 128
7.7. Step 1, Proposition 26: the operations ± 131
7.8. Step 1, Propositions 27 and 28: some 1 types 133
Chapter 8. Theorems 7.6 7.9 138
8.1. Step 2. Theorems 7.6 and 7.7 138
8.2. Step 5. Theorem 7.9.7 : extending a direct sum 141
8.3. Step 3. Theorem 7.8, 1 types over sums 141
8.4. Theorem 7.8, conclusion 144
Appendix: Examples for richer languages 150
Bibliography 154
Index of Notation 158
Index 159
|
| any_adam_object | 1 |
| author | Cherlin, Gregory L. 1948- |
| author_GND | (DE-588)172031974 |
| author_facet | Cherlin, Gregory L. 1948- |
| author_role | aut |
| author_sort | Cherlin, Gregory L. 1948- |
| author_variant | g l c gl glc |
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| dewey-full | 511/.5 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics 510 - Mathematics |
| dewey-raw | 511/.5 510 |
| dewey-search | 511/.5 510 |
| dewey-sort | 3511 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011934970 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:21:19Z |
| institution | BVB |
| isbn | 0821808362 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008067207 |
| oclc_num | 37675657 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-29T DE-739 DE-384 DE-20 DE-91G DE-BY-TUM DE-83 DE-11 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-29T DE-739 DE-384 DE-20 DE-91G DE-BY-TUM DE-83 DE-11 DE-188 |
| physical | XIII, 161 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | American Mathematical Society: Memoirs of the American Mathematical Society |
| series2 | American Mathematical Society: Memoirs of the American Mathematical Society |
| spellingShingle | Cherlin, Gregory L. 1948- The classification of countable homogeneous directed graphs and countable homogeneous n-tournaments American Mathematical Society: Memoirs of the American Mathematical Society Permutatiegroepen gtt Teoria dos grafos larpcal Directed graphs Model theory Permutation groups Ramsey theory Tournaments (Graph theory) Gerichteter Graph (DE-588)4156815-1 gnd Turnier Mathematik (DE-588)4473306-9 gnd Modelltheorie (DE-588)4114617-7 gnd Permutationsgruppe (DE-588)4173833-0 gnd Ramsey-Theorie (DE-588)4212682-4 gnd |
| subject_GND | (DE-588)4156815-1 (DE-588)4473306-9 (DE-588)4114617-7 (DE-588)4173833-0 (DE-588)4212682-4 |
| title | The classification of countable homogeneous directed graphs and countable homogeneous n-tournaments |
| title_auth | The classification of countable homogeneous directed graphs and countable homogeneous n-tournaments |
| title_exact_search | The classification of countable homogeneous directed graphs and countable homogeneous n-tournaments |
| title_full | The classification of countable homogeneous directed graphs and countable homogeneous n-tournaments Gregory L. Cherlin |
| title_fullStr | The classification of countable homogeneous directed graphs and countable homogeneous n-tournaments Gregory L. Cherlin |
| title_full_unstemmed | The classification of countable homogeneous directed graphs and countable homogeneous n-tournaments Gregory L. Cherlin |
| title_short | The classification of countable homogeneous directed graphs and countable homogeneous n-tournaments |
| title_sort | the classification of countable homogeneous directed graphs and countable homogeneous n tournaments |
| topic | Permutatiegroepen gtt Teoria dos grafos larpcal Directed graphs Model theory Permutation groups Ramsey theory Tournaments (Graph theory) Gerichteter Graph (DE-588)4156815-1 gnd Turnier Mathematik (DE-588)4473306-9 gnd Modelltheorie (DE-588)4114617-7 gnd Permutationsgruppe (DE-588)4173833-0 gnd Ramsey-Theorie (DE-588)4212682-4 gnd |
| topic_facet | Permutatiegroepen Teoria dos grafos Directed graphs Model theory Permutation groups Ramsey theory Tournaments (Graph theory) Gerichteter Graph Turnier Mathematik Modelltheorie Permutationsgruppe Ramsey-Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008067207&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT cherlingregoryl theclassificationofcountablehomogeneousdirectedgraphsandcountablehomogeneousntournaments |
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