The Reconstruction of Cycle-free Partial Orders from their Abstract Automorphism Groups II : Cone Transitive CFPOs
Abstract
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 middle paper, we adapt a method used by Shelah in ShelahPermutation and ShelahPermutationErrata, and by Shelah and Truss in ShelahTrussQuotients to define a cone transitive CFPO inside its automorphism group using the language of group theory.
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