Absolute and Relative Properties of Negatively Numbered Families

M. Kh Faizrahmanov, V. G. Puzarenko

Research output: Contribution to journalArticlepeer-review

Abstract

We study in this paper negative A-numberings where A are admissible structures. We establish that a series of classical assumptions is remained to hold for negative A-numberings in the case of the application of certain limits as for numberings as for admissible structures. We find examples of admissible structures A whose families of all Σ-subsets have negative non-decidable minimal computable A-numberings. The admissible structures from this series have negative computable A-numberings whose numbered equivalence differs from corresponding ones of any computable A-numbering of family of total functions.

Original languageEnglish
Article number6
Pages (from-to)726-734
Number of pages9
JournalLobachevskii Journal of Mathematics
Volume42
Issue number4
DOIs
Publication statusPublished - Apr 2021

Keywords

  • admissible structure
  • analytic hierarchy
  • equivalence
  • hyperarithmetical sets
  • minimal numbering
  • negative numbering
  • numbering

OECD FOS+WOS

  • 1.01 MATHEMATICS

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