Long range actions, connectedness, and dismantlability in relational structures.

In this paper we study alternative characterizations of dismantlability properties of relational structures in terms of various connectedness and mixing notions. We relate these results with earlier work of Brightwell and Winkler, providing a generalization from the graph case to the general relational structure context. In addition, we develop properties related to what we call (presence or absence of) boundary long range actions and the study of valid extensions of a given partially defined homomorphism, an approach that turns out to be novel even in the graph case. Finally, we also establish connections between these results and spatial mixing properties of Gibbs measures, the topological strong spatial mixing condition introduced by Briceno, and a characterization of finite duality due to Larose, Loten, and Tardif.