Jump inversions of algebraic structures and Σ-definability

Marat Faizrahmanov, Asher Kach, Iskander Kalimullin, Antonio Montalbán, Vadim Puzarenko

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

It is proved that for every countable structure A and a computable successor ordinal α there is a countable structure A−α which is (Formula presented.) -least among all countable structures C such that A is Σ-definable in the αth jump C(α). We also show that this result does not hold for the limit ordinal α = ω. Moreover, we prove that there is no countable structure A with the degree spectrum (Formula presented.) for (Formula presented.).

Original languageEnglish
Pages (from-to)37-45
Number of pages9
JournalMathematical Logic Quarterly
Volume65
Issue number1
DOIs
Publication statusPublished - 1 May 2019

Keywords

  • THEOREM
  • REDUCIBILITY

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