The classification of homogeneous finite-dimensional permutation structures

TL;DR

This paper classifies all homogeneous finite-dimensional permutation structures in finitely many linear orders, confirming a longstanding conjecture and building on prior model-theoretic work to provide a nearly complete classification.

Contribution

It provides a nearly complete classification of homogeneous finite-dimensional permutation structures, extending previous results and confirming the conjectured structure.

Findings

Primitive case proven using model-theoretic methods

Nearly complete classification achieved

Confirms the classification conjecture by the first author

Abstract

We classify the homogeneous finite-dimensional permutation structures, i.e., homogeneous structures in a language of finitely many linear orders, giving a nearly complete answer to a question of Cameron, and confirming the classification conjectured by the first author. The primitive case was proven by the second author using model-theoretic methods, and those methods continue to appear here.