Before revision:  Building on Logical Compactness, in a revealed-preference setting, we reprove Reny's infinite-data version of Afriat's theorem and (newly) prove an infinite-data version of McFadden and Richter's characterization of rationalizable stochastic datasets. In a matching setting, we reprove large-market existence results implied by Fleiner's analysis, and  prove both the strategy-proofness of the man-optimal stable mechanism in infinite markets , and an infinite-market version of Nguyen and Vohra's existence result for near-feasible stable matchings with couples.
After revision:  Building on Logical Compactness, in a matching setting, we reprove large-market existence results implied by Fleiner's analysis, and prove both the strategy-proofness of the man-optimal stable mechanism in infinite markets , and an infinite-market version of Nguyen and Vohra's existence result for near-feasible stable matchings with couples.