Homogeneous Ordered Graphs, Metrically Homogeneous Graphs, and Beyond 2 Volume Hardback Set
Cambridge University Press
978-1-009-23018-6 (ISBN)
These two volumes by Professor Cherlin present the state of the art in the classification of homogeneous structures in binary languages and related problems in the intersection of model theory and combinatorics. Researchers and graduate students in the area will find in these volumes many far-reaching results and interesting new research directions to pursue. In Volume I, the homogeneous ordered graphs are classified, a new family of metrically homogeneous graphs is constructed, and a general classification conjecture is presented, together with general structure theory and applications to a general classification conjecture for such graphs. Volume II continues the analysis into more general expansions of graphs or tournaments by an additional binary relation, called 3-multi-graphs or 3-multi-tournaments, applying and extending the results of Volume I, resulting in a detailed catalogue of such structures and a second classification conjecture. Appendices to both volumes explore recent developments and open questions.
Gregory Cherlin is Distinguished Professor Emeritus at Rutgers University. He has worked on applications of model theory to algebra and combinatorics for half a century, and has published four books and over 100 articles on model theory and its applications.
Volume I: 1. Results; 2. Methods; Part I. Homogeneous Ordered Graphs: 3. The catalog of homogeneous ordered graphs; 4. The generically ordered local order; 5. Ordered homogeneous graphs: Plan of the proof, Propositions I–IX; 6. Ordered homogeneous graphs: Proposition I; 7. Ordered homogeneous graphs: Proposition II; 8. Ordered homogeneous graphs: Proposition III; 9. Ordered homogeneous graphs: Proposition IV; 10. Ordered homogeneous graphs: Proposition V; Part II. Metrically Homogeneous Graphs: 11. Metrically homogeneous graphs: preliminaries; 12. Admissibility allows amalgamation; 13. Triangle constraints and 4-triviality; 14. Amalgamation requires admissibility; 15. Local analysis; 16. The bipartite case; 17. Infinite diameter; Appendix A. Some recent advances; References for Volume I; Index; Volume II: 18. Classification problems for small binary languages; 19. Homogeneous 3-multi-graphs; 20. Imprimitive homogeneous 2-multi-tournaments; 21. 3-constrained homogeneous 2-multi-tournaments; 22. Homogeneous 2-multi-tournaments: forbidden triangles; Conclusion; Appendix B. Open problems and some recent results; References for Volume II; Index.
| Erscheint lt. Verlag | 31.7.2022 |
|---|---|
| Reihe/Serie | Lecture Notes in Logic |
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 157 x 235 mm |
| Gewicht | 1200 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre |
| ISBN-10 | 1-009-23018-2 / 1009230182 |
| ISBN-13 | 978-1-009-23018-6 / 9781009230186 |
| Zustand | Neuware |
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