Lecture Notes in Logic, 53

Homogenous Ordered Graphs, Metrically Homogenous Graphs, and Beyond: Volume 1, Ordered Graphs and Distanced Graphs

Gregory Cherlin

Year: 2022
ISBN: 9781009229692
386 pages, Hardcover
Buy now  (when ordering, include the discount code ASL25 to receive the 25% ASL member discount). You can also purchase the multiple copy pack of both volumes in this set at a reduced price.


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.


Table of Contents

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