Minimality conditions on circularly ordered structures

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. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Countably categorical weakly o-minimal structures of finite convexity rank

We completely describe countably categorical weakly o-minimal theories of finite convexity rank.     

Binary types in ℵ0‐categorical weakly o‐minimal theories

Orthogonality of all families of pairwise weakly orthogonal 1‐types for ?₀‐categorical weakly o‐minimal theories of finite convexity rank has been proved in 6 . Here we prove orthogonality of all such families for binary 1‐types in an arbitrary ?₀‐categorical weakly o‐minimal theory and give an extended criterion for binarity of ?₀‐categorical weakly o‐minimal theories (additionally in terms of binarity of 1‐types). © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Preservation of <Emphasis Type="Italic">ω</Emphasis>-Categoricity In Expanding The Models of Weakly <Emphasis Type="Italic">o</Emphasis>-Minimal Theories

Studying the model-theoretic properties that are preserved under expansion of the models of countably categorical weakly o-minimal theories of finite convexity rank with convex unary predicates, we show that countable categoricity and convexity rank are among these properties.     

A Criterion for Binarity of Almost $ \omega $ -Categorical Weakly $ o $ -Minimal Theories

Siberian Mathematical Journal - Continuing the study of weak $ o $ -minimality, we prove a theorem on the behavior of a definable unary function on the set of realizations of a nonalgebraic 1-type...