Computable Positive and Friedberg Numberings in Hyperarithmetic

I. Sh Kalimullin, V. G. Puzarenko, M. Kh Faizrakhmanov

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We point out an existence criterion for positive computable total Π11 -numberings of families of subsets of a given Π11 -set. In particular, it is stated that the family of all Π11 -sets has no positive computable total Π11 -numberings. Also we obtain a criterion of existence for computable Friedberg Σ11 -numberings of families of subsets of a given Σ11 - set, the consequence of which is the absence of a computable Friedberg Σ11 -numbering of the family of all Σ11 -sets. Questions concerning the existence of negative computable Π11 - and Σ11 -numberings of the families mentioned are considered.

Original languageEnglish
Pages (from-to)46-58
Number of pages13
JournalAlgebra and Logic
Volume59
Issue number1
DOIs
Publication statusPublished - 1 Mar 2020

Keywords

  • admissible set
  • analytical hierarchy
  • computable numbering
  • Friedberg numbering
  • negative numbering
  • positive numbering
  • FAMILIES
  • PRESENTATIONS

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