When a linear order has an order preserving surjection onto each of its suborders, we say that it is strongly surjective. I will mainly talk about countable strongly surjective linear orders, outlining the proof that they form a complete set for the class of unions of an analytic and a coanalytic set. I will then discuss the case of uncountable strongly surjective orders.
This is a joint work with Riccardo Camerlo and Alberto Marcone.