  It is well-known that every transitive linear order is exponentiable.
However, is the converse true? This question was posed in Chapter 8 of the
textbook titled "Linear Orderings" by Rosenstein. We define the class CTLO of
cyclically transitive linear orders that properly contains the class of
transitive linear orders, and show that all discrete unbounded orders in CTLO
are exponentiable, thereby providing a negative answer to the question. The
class CTLO is closely related to the class of transitive cyclic orders
introduced by Droste, Giraudet and Macpherson. We also discuss the closure of
subclasses of CTLO under products and iterated Hausdorff condensations.
