Omega-categorical limits of betweenness relations and D-sets

2024/10/08 by Asma Ibrahim Almazaydeh, Almazaydeh, Asma Ibrahim, Samuel Braunfeld +3
Computer Science · #Advanced Algebra and Logic #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2410.05832

openalex publication_date 2024/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We explore two constructions of oligomorphic Jordan permutation groups preserving a `limit of betweenness relations' and a `limit of D-relations', from \citebhattmacph2006jordan and \citealmazaydeh2021jordan respectively. Several issues left open in \citealmazaydeh2021jordan are resolved. In particular it is shown that the `limit of D-relations' is not homogeneous in the given language, but is `homogenizable', that is, there is a homogeneous structure over a finite relational language with the same universe and the same automorphism group. The structure is NIP, but not monadically NIP, its age is not well-quasi-ordered under embeddability, and the growth rate of the sequence enumerating orbits on k-sets grows faster than exponentially. The automorphism group is maximal-closed in the symmetric group. Similar results are shown for the construction in \citebhattmacph2006jordan.

Related

• Jordan permutation groups and limits of D-relations
• On omega-categorical structures with few finite substructures
• On limits of betweenness relations
• Universal homogeneous constraint structures and the hom-equivalence classes of weakly oligomorphic structures
• Infinite Limits of Finite-Dimensional Permutation Structures, and their Automorphism Groups: Between Model Theory and Combinatorics