Algorithmic properties of branching models

Abstract

This paper is a continuation of the study of the branching properties of models [i]. We generalize the very concept of branching, and thus we are able to apply the basic theorems to a wider class of models.The study of branching models enables us to consider, from a unique point of view, many earlier results on the hyperimmunity of sets of atoms in Boolean algebras [2,3], on the complexity of ~ and ~)'in ~+~' , and on the relation of succession in linear orderings [5] (see [4]).Moreover, using Theorem i, we obtain a characterization of autostable dense linear orderings with a one-place predicate.

Preface

“…In [18] Khoussainov provided examples of structures of type (A, h) where h is a function from A to A, of computable dimension n with n ∈ ω. In [28] Ventsov studied computable dimensions of (L; ≤, P) where (L; ≤) is a linearly ordered set and P is a unary predicate. This paper is a continuation of the above work with an emphasis on computable dimensions of linearly ordered sets with distinguished endomorphisms.…”