The Reconstruction of Cycle-free Partial Orders from their Abstract Automorphism Groups II : Cone Transitive CFPOs

Robert Barham

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arXiv · 1502.03219

The Reconstruction of Cycle-free Partial Orders from their Abstract Automorphism Groups II : Cone Transitive CFPOs

Robert Barham

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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 \cite{ShelahPermutation} and \cite{ShelahPermutationErrata}, and by Shelah and Truss in \cite{ShelahTrussQuotients} to define a cone transitive CFPO inside its automorphism group using the language of group theory.

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Robert Barham. 2015-03-12. The Reconstruction of Cycle-free Partial Orders from their Abstract Automorphism Groups II : Cone Transitive CFPOs. https://arxiv.org/abs/1502.03219

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