On computable self-embeddings of computable linear orderings

Abstract

AbstractWe solve a longstanding question of Rosenstein, and make progress toward solving a long-standing open problem in the area of computable linear orderings by showing that every computable η-like linear ordering without an infinite strongly η-like interval has a computable copy without nontrivial computable self-embedding.The precise characterization of those computable linear orderings which have computable copies without nontrivial computable self-embedding remains open.