✦ LIBER ✦

A note on partial numberings

✍ Scribed by Serikzhan Badaev; Dieter Spreen

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 127 KB
Volume: 51
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200310131

No coin nor oath required. For personal study only.

✦ Synopsis

Dedicated to Klaus Weihrauch on the occasion of his 60th birthday.

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.

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