E -combinations of ℵ 0 -categorical linear orderings

Abstract

In a series of S.V. Sudoplatov’s works the topological properties of families of theories are
studied. He introduced the concepts of the P-operator and the E-operator, allowing to study
the connections between theories regarding suitable closure operators. These operators make it
possible to generate new theories by means of the considered families of theories, and also find in
some cases minimal or smallest generating sets. This research was continued in collaborative work
of B.Sh. Kulpeshov and S.V. Sudoplatov for families of ordered theories, including families of
quite o-minimal theories. This article explores the E-combinations of countably many countably
categorical linearly ordered structures of pure linear order. Criterion for countable categoricity
of E-combination of countably many copies of an arbitrary countably categorical linear order is
obtained. As a consequence, a description of the countable spectrum of such a combination is
obtained.