Note on generated choice and axioms of revealed preference

In this article, we study the axiomatic foundations of revealed preference theory. Let P denote the strict and R the weak revealed preference, respectively. The purpose of the paper is to show that weak, strong, and Hansson's axiom of revealed preference can be given as c^Pm = c^Rg, c^t(P)m = c^Rg, and c^t(R)g = c^Pm, respectively. Here, t is the operator of the transitive closure, c^Pm and c^Rg are the generated choices in terms of maximality and in terms of greatestness.