Order Relations Over Finitely Supported Structures

We present some properties of the order relations in the framework of finitely supported structures. We particularly analyze partially ordered sets, lattices and Galois connections, presenting specific properties (regarding cardinality order, cardinality arithmetic and fixed points) in the framework of finitely supported algebraic structures, as well as properties that are naturally extended from the classical Zermelo-Fraenkel framework by replacing 'structure' with 'atomic finitely supported structure'.