  In this triple of papers, we examine when two cycle-free partial orders can
share an abstract automorphism group. This question was posed by M. Rubin in
his memoir concerning the reconstruction of trees.
  In this first paper, we give a variety of conditions that guarantee when a
CFPO shares an automorphism group with a tree. Some of these conditions are
conditions on the abstract automorphism group, while some are one the CFPO
itself. Some of the lemmas used have corollaries concerning the model theoretic
properties of a CFPO.
