Pseudofinite primitive permutation groups acting on one-dimensional sets

TL;DR

This paper classifies pseudofinite primitive permutation groups acting on one-dimensional sets within a specific model-theoretic framework, extending previous classifications to theories of infinite rank.

Contribution

It generalizes the classification of pseudofinite definably primitive permutation groups from finite to infinite rank supersimple theories.

Findings

Classification of pseudofinite primitive permutation groups under new conditions

Extension of previous finite rank results to infinite rank theories

Identification of structural properties of these groups

Abstract

Working in a theory with an integer-valued dimension on interpretable sets, we classify pseudofinite definably primitive permutation groups acting on one-dimensional sets which satisfy a version of chain condition on centralizers and on point-wise stabilizers. This generalises the classification of pseudofinite definably primitive permutation groups in supersimple theories of finite rank to supersimple theories of infinite rank.