Mathematical Logic Quarterly 51 (2):129-136 (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
Keywords total numberings  Rogers (semi) lattice  Partial numberings  computable numberings of effective topological spaces
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DOI 10.1002/malq.200310131
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References found in this work BETA

Theorie der Numerierungen I.Ju L. Eršov - 1973 - Mathematical Logic Quarterly 19 (19‐25):289-388.
Theorie der Numerierungen II.J. U. L. Eršov - 1975 - Mathematical Logic Quarterly 21 (1):473-584.
On Effective Topological Spaces.Dieter Spreen - 1998 - Journal of Symbolic Logic 63 (1):185-221.
Effective Inseparability in a Topological Setting.Dieter Spreen - 1996 - Annals of Pure and Applied Logic 80 (3):257-275.
On Effective Topological Spaces.Dieter Spreen - 1998 - Journal of Symbolic Logic 63 (1):185-221.

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Strong Reducibility of Partial Numberings.Dieter Spreen - 2005 - Archive for Mathematical Logic 44 (2):209-217.

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