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  3. Homogeneous Ordered Graphs, Metrically Homogeneous Graphs, and Beyond
  • Cited by 1
  • Volume 1: Ordered Graphs and Distanced Graphs
  • Gregory Cherlin, Rutgers University, New Jersey
Publisher:
Cambridge University Press
Online publication date:
June 2022
Print publication year:
2022
Online ISBN:
9781009229661
DOI:
https://doi.org/10.1017/9781009229661
Subjects:
Mathematics, Logic, Categories and Sets, Discrete Mathematics Information Theory and Coding, Programming Languages and Applied Logic
Series:
Lecture Notes in Logic (53)
Information

Book 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.

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