Jump inversions of algebraic structures and Σ-definability

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

doi:10.1002/malq.201800015

Jump inversions of algebraic structures and Σ-definability

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

Кафедра математических наук ММФ и СУНЦ НГУ

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	37-45
Number of pages	9
Journal	Mathematical Logic Quarterly
Volume	65
Issue number	1
DOIs	https://doi.org/10.1002/malq.201800015
Publication status	Published - 1 May 2019

Keywords

THEOREM
REDUCIBILITY

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10.1002/malq.201800015

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AU - Puzarenko, Vadim

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N2 - 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.).

AB - 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.).

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Jump inversions of algebraic structures and Σ-definability

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Keywords

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