A permutation group acting transitively on certain collections of models

Samuel M. Corson; Saharon Shelah

doi:10.1016/j.ejc.2026.104415

A permutation group acting transitively on certain collections of models

Samuel M. Corson^*
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

It is shown, from σ-centered Martin’s Axiom, that there exists a proper dense subgroup of the symmetric group on a countably infinite set whose natural action on sufficiently flexible relational structures is transitive. This allows us to give consistent positive answers to some questions of Peter M. Neumann from the 1980s.

Original language	English
Article number	104415
Journal	European Journal of Combinatorics
Volume	137
DOIs	https://doi.org/10.1016/j.ejc.2026.104415
State	Published - Sep 2026

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© 2026 The Author(s).

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10.1016/j.ejc.2026.104415

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A permutation group acting transitively on certain collections of models

Abstract

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