Homogeneous Ordered Graphs, Metrically Homogeneous Graphs, and Beyond: Volume 2, 3-Multi-graphs and 2-Multi-tournaments (Lecture Notes in Logic, Series Number 54)

This is the second 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. This volume continues the analysis of the first volume to 3-multi-graphs and 3-multi-tournaments, expansions of graphs and tournaments by the addition of a further binary relation. The opening chapter provides an overview of the volume, outlining the relevant results and conjectures. The author applies and extends the results of Volume I to obtain a detailed catalogue of such structures and a second classification conjecture. The book ends with an appendix exploring recent advances and open problems in the theory of homogeneous structures and related subjects.

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.