2005/06/08 by Beibut Sh. Kulpeshov, Dugald Macpherson · 3 citations
Mathematics · Computer Science · #Advanced Topology and Set Theory #Rings, Modules, and Algebras #Advanced Algebra and Logic #Homogeneous #Mathematics #Transitive relation #Categorical variable #Order (exchange) #Permutation (music) #Combinatorics #Permutation group #Pure mathematics #Physics #Statistics
paper · doi:10.1002/malq.200410040
openalex publication_date 2005/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/07
We explore analogues of o-minimality and weak o-minimality for circularly ordered sets. Much of the theory goes through almost unchanged, since over a parameter the circular order yields a definable linear order. Working over ∅︁ there are differences. Our main result is a structure theory (with infinitely many doubly transitive examples related to Jordan permutation groups) for ℵ0-categorical weakly circularly minimal structures. There is a 5-homogeneous (or ‘5-indiscernible’) example which is not 6-homogeneous, but any example which is k-homogeneous for some k ≥ 6 is k-homogeneous for all k. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)