Acknowledgements Throughout the writing and preparation of this paper I have been in- debted to many people, all of whom have helped and contributed much. A few need to be mentioned specifically. Many others should be mentioned, but I have erred on the side of brevity. Everyone has my thanks. Firstly, there is John Truss, my Ph.D. supervisor. Without his help and encouragement, this paper would never have been completed. In addition he edited the final version and wrote the extended introduction. I would also like to thank Alan and Audrey West, as they have been an invaluable help in the preparation of the document. I also thank the Department of Pure Mathematics at Leeds for their continued support over the last three years. Finally, I would like to thank my wife Dorothy, as she has had to put up with me throughout the whole process. June 1995 Key words and phrases, cycle-free partial order, transitive, homogeneous, tree, classification. x
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