The enumeration spectrum hierarchy of n-families

Abstract

© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimWe introduce a hierarchy of sets which can be derived from the integers using countable collections. Such families can be coded into countable algebraic structures preserving their algorithmic properties. We prove that for different finite levels of the hierarchy the corresponding algebraic structures have different classes of possible degree spectra.