Friedberg numberings of families of partial computable functionals

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Abstract

We consider computable numberings of families of partial computable functionals of finite types. We show, that if a family of all partial computable functionals of type 0 has a computable friedberg numbering, then family of all partial computable functionals of any given type also has computable friedberg numbering. Furthermore, for a type σ | τ there are infinitely many nonequivalent computable minimal nonpositive, positive nondecidable and friedberg numberings.

Translated title of the contributionФридберговы нумерации семейств частично вычислимых функционалов
Original languageEnglish
Pages (from-to)331-339
Number of pages9
JournalСибирские электронные математические известия
Volume16
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • partial computable functionals
  • computable morphisms
  • computable numberings
  • Rogers semilattice
  • minimal numbering
  • positive numbering
  • friedberg numbering

OECD FOS+WOS

  • 1.01 MATHEMATICS

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