Minimality conditions on circularly ordered structures

摘要

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 0-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.