Before revision:   Here, we show how to extend key results from (finite) models of matching, games on graphs, and trading networks to infinite models by way of Logical Compactness, a core result from Propositional Logic.
After revision:  Such assumptions introduce a conceptual problem, as results that rely on finiteness are often implicitly nonrobust; for example, they may rely on edge effects or artificial boundary conditions. Here, we show how to extend key results from (finite) models of matching, games on graphs, and trading networks to infinite models by way of Logical Compactness, a core result from Propositional Logic.