Set Theory and Logic

    

Fixed Point Properties of Precompletely and Positively Numbered Sets

Authors: Marat Faizrahmanov

In this paper, we prove a joint generalization of Arslanov’s completenesscriterion and Visser’s ADN theorem for precomplete numberings. Then we considerthe properties of completeness and precompleteness of numberings in the context ofthe positivity property. We show that the completions of positive numberings are nottheir minimal covers and that the Turing completeness of any set A is equivalent to theexistence of a positive precomplete A-computable numbering of any infinite family withpositive A-computable numbering.

Comments: 14 Pages.

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Submission history

[v1] 2023-12-17 08:58:52

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