On Weakly Coholographic Structures

We introduce and study the notion of weak coholographicity, which generalizes the concept of holographicity and is, in a certain sense, dual to the notion of weak holographicity. We describe weakly coholographic fields and abelian groups, and prove that all ordinals, equivalence relations, and countable Boolean algebras are weakly coholographic. A complete picture is given of the relationships among the properties of holographicity, weak holographicity, weak coholographicity, and countable categoricity.