
Homogeneous Ordered Graphs, Metrically Homogeneous Graphs, and Beyond: Volume 1, Ordered Graphs and Distanced Graphs
Gregory Cherlin(Author)
Cambridge University Press
Published on 7. July 2022
Book
Hardback
386 pages
978-1-009-22969-2 (ISBN)
Description
This is the first of two volumes by Professor Cherlin presenting 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 this volume, Cherlin develops a complete classification of homogeneous ordered graphs and provides a full proof. He then proposes a new family of metrically homogeneous graphs, a weakening of the usual homogeneity condition. A general classification conjecture is presented, together with general structure theory and applications to a general classification conjecture for such graphs. It also includes introductory chapters giving an overview of the results and methods of both volumes, and an appendix surveying recent developments in the area. An extensive accompanying bibliography of related literature, organized by topic, is available online.
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Edition type
New edition
Product notice
sewn/stitched
Cloth over boards
Illustrations
Worked examples or Exercises
Dimensions
Height: 230 mm
Width: 150 mm
Thickness: 26 mm
Weight
612 gr
ISBN-13
978-1-009-22969-2 (9781009229692)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
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Other editions
Additional editions

Gregory Cherlin
Homogeneous Ordered Graphs, Metrically Homogeneous Graphs, and Beyond: Volume 1, Ordered Graphs and Distanced Graphs
E-Book
06/2022
Cambridge University Press
€136.99
Available for download
Person
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.
Content
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.