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This paper is concerned with the axiomatic foundation of the revealed preference theory. Many well-known results in literature rest upon the ability to choose over budget sets that contains only 2 or 3 elements, the situations which are not observable in real life. In order to give a more realistic approach, this paper shows that many of the famous consistency requirements, such as those proposed by Arrow, Sen, Samuelson etc., are equivalent if the domain of choice functions satisfy some set theoretical properties. And these properties, unions and inclusions for example, are proposed in a way that gives observability.

A Generalized Unification Theorem for Choice Theoretic Foundations: Avoiding the Necessity of Pairs and Triplets