Lexicographic preferences representable by real-branching trees with countable height: A dichotomy result

On the representability number of lexicographic products in a Dedekind-complete chain

“…This fact is relevant in view of a possible classification of (short) chains according to their representability number in R (cf. [7,8]). Furthermore, the results obtained here can be useful to provide some insight into the topic of lexicographic preferences and their representability by (extended forms of) utility functions: see, e.g., [1,2,4] for lexicographic preferences, and [3] for an overview of the topic of representability.…”