A note on partial numberings
S. A. Badaev, Dieter Spreen · Mathematical logic quarterly · 2005
The different behaviour of total and partial numberings with respect to the reducibility preorder is investigated. Partial numberings appear quite naturally in computability studies for topological spaces. The degrees of partial numberings form a distributive lattice which in the case of an infinite numbered set is neither complete nor contains a least element. Friedberg numberings are no longer minimal in this situation. Indeed, there is an infinite descending chain of non-equivalent Friedberg numberings below every given numbering, as well as an uncountable antichain. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)