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The Classification of Countable Homogeneous Directed Graphs and Countable Homogeneous $$n$$-tournaments
Gregory L. Cherlin, Rutgers University, New Brunswick, NJ
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Memoirs of the American Mathematical Society
1998; 161 pp; softcover
Volume: 131
ISBN-10: 0-8218-0836-2
ISBN-13: 978-0-8218-0836-8
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

Graduate students and mathematicians interested in model theory, combinatorics, infinite permutation and group theory.

• 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 7.6-7.9
• Appendix: Examples for richer languages
• Bibliography
• Index of Notation
• Index