Linear orders: when embeddability and epimorphism agree

Abstract

When a linear order has an order preserving surjection onto each of its suborders we say that it is strongly surjective. We prove that the set of countable strongly surjective linear orders is complete for the class of sets which are the union of an analytic and a coanalytic set. Using hypotheses beyond ZFC, we prove the existence of uncountable strongly surjective orders.

32 pages; v2 is the "accepted author manuscript" - an author-created version of the final journal article (to reflect changes made in peer review and editing)

References in corpus (1)

• Epimorphisms between linear orders

Cited by in corpus (3)

• Polish metric spaces with fixed distance set
• Convex Embeddability and Knot Theory
• Piecewise convex embeddability on linear orders