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
Finally, I would like to thank my wife Dorothy, as she has had to put
up with me throughout the whole process.
Key words and phrases, cycle-free partial order, transitive, homogeneous, tree,