Low linear orderings

Abstract

We say that L is weakly η-like if L/∼ is isomorphic to the natural ordering of rational numbers. We construct a computable presentation of any low weakly η-like linear ordering with no strongly η-like interval. Also we prove that there exists a noncomputably presentable low2 weakly η-like linear ordering with no strongly η-like interval. © ; 2010 The Author. Published by Oxford University Press. All rights reserved.