Limitwise monotonic sets of reals

Abstract

© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. We extend the limitwise monotonicity notion to the case of arbitrary computable linear ordering to get a set which is limitwise monotonic precisely in the non-computable degrees. Also we get a series of connected non-uniformity results to obtain new examples of non-uniformly equivalent families of computable sets with the same enumeration degree spectrum.