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Preprint Number 1430
1430. Samuel Braunfeld Infinite Limits of Finite-Dimensional Permutation Structures, and their
Automorphism Groups: Between Model Theory and Combinatorics E-mail: Submission date: 11 May 2018 Abstract: The author's thesis. Much of the first 8 chapters appeared in the previous articles “The Lattice of Definable Equivalence Relations in Homogeneous n-Dimensional Permutation Structures”, “Ramsey expansions of Λ-ultrametric spaces”, and “Homogeneous 3-dimensional permutation structures” In the course of classifying the homogeneous permutations, Cameron introduced
the viewpoint of permutations as structures in a language of two linear orders,
and this structural viewpoint is taken up here. The majority of this thesis is
concerned with Cameron's problem of classifying the homogeneous structures in a
language of finitely many linear orders, which we call finite-dimensional
permutation structures. Towards this problem, we present a construction that we
conjecture produces all such structures. Some evidence for this conjecture is
given, including the classification of the homogeneous 3-dimensional
permutation structures. Mathematics Subject Classification: 03C13, 03C15, 03C50, 05D10, 37B05 Keywords and phrases: |

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