Memoirs of the American Mathematical Society 1998; 161 pp; softcover Volume: 131 ISBN10: 0821808362 ISBN13: 9780821808368 List Price: US$54 Individual Members: US$32.40 Institutional Members: US$43.20 Order Code: MEMO/131/621
 In this book, Ramsey theoretic methods introduced by Lachlan are applied to classify the countable homogeneous directed graphs. This is an uncountable collection, and this book presents the first explicit classification result covering an uncountable family. The author's aim is to demonstrate the potential of Lachlan's method for systematic use. Features:  Interface between combinatorics and model theory
 Unusual use of Ramsey's theorem to classify structures
 An extension of an already elaborate branch of model theory
 The first monograph on Lachlan's method
Readership Graduate students and mathematicians interested in model theory, combinatorics, infinite permutation and group theory. Table of Contents  Results and open problems
 Homogeneous \(2\)tournaments
 Homogeneous \(n\)tournaments
 Homogeneous symmetric graphs
 Homogeneous directed graphs omitting \(I_\infty\)
 Propositions \(16\) to \(20\) and MT \(2.2\)
 Homogeneous directed graphs embedding \(I_\infty\)
 Theorems 7.67.9
 Appendix: Examples for richer languages
 Bibliography
 Index of Notation
 Index
