Many economic-theoretic models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. Such assumptions introduce a conceptual problem, as results that rely on finiteness are often implicitly nonrobust; for example, they may depend upon edge effects or artificial boundary conditions. Here, we present a unified method that enables us to remove finiteness assumptions, such as those on market sizes, time horizons, and datasets. We then apply our approach to a variety of matching, exchange economy, and revealed preference settings. The key to our approach is Logical Compactness, a core result from Propositional Logic. Building on Logical Compactness, in a matching setting, we reprove large-market existence results implied by Fleiners analysis, and (newly) prove both the strategy-proofness of the man-optimal stable mechanism in infinite markets and an infinite-market version of Nguyen and Vohras existence result for near-feasible stable matchings with couples. In a trading-network setting, we prove that the Hatfield et al. result on existence of Walrasian equilibria extends to infinite markets. In a dynamic matching setting, we prove that Pereyras existence result for dynamic two-sided matching markets extends to a doubly infinite time horizon. Finally, beyond existence and characterization of solutions, in a revealed-preference setting we reprove Renys infinite-data version of Afriats theorem and (newly) prove an infinite-data version of McFadden and Richters characterization of rationalizable stochastic datasets.
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