Abstract
Abstract : This paper is concerned with the axiomatic foundations of the theory of choice. The theorems that proved established the existence of a relationship between the transitivity of preference and the structure of certain sets in the choice space that are defined with respect to preference. The central results are contained in two theorems that state conditions under which the transitivity of I is sufficient to imply the transitivity of R. An improved version of Rader's lemma is used to make the proof of these theorems simpler, and a theorem that is intimately related to Uzawa's lemma is also proved.
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