Jump inversions of algebraic structures and Σ-definability

Standard

Jump inversions of algebraic structures and Σ-definability. / Faizrahmanov, Marat; Kach, Asher; Kalimullin, Iskander et al.

In: Mathematical Logic Quarterly, Vol. 65, No. 1, 01.05.2019, p. 37-45.

Research output: Contribution to journal › Article › peer-review

Harvard

Faizrahmanov, M, Kach, A, Kalimullin, I, Montalbán, A & Puzarenko, V 2019, 'Jump inversions of algebraic structures and Σ-definability', Mathematical Logic Quarterly, vol. 65, no. 1, pp. 37-45. https://doi.org/10.1002/malq.201800015

APA

Faizrahmanov, M., Kach, A., Kalimullin, I., Montalbán, A., & Puzarenko, V. (2019). Jump inversions of algebraic structures and Σ-definability. Mathematical Logic Quarterly, 65(1), 37-45. https://doi.org/10.1002/malq.201800015

Vancouver

Faizrahmanov M, Kach A, Kalimullin I, Montalbán A, Puzarenko V. Jump inversions of algebraic structures and Σ-definability. Mathematical Logic Quarterly. 2019 May 1;65(1):37-45. doi: 10.1002/malq.201800015

Author

Faizrahmanov, Marat ; Kach, Asher ; Kalimullin, Iskander et al. / Jump inversions of algebraic structures and Σ-definability. In: Mathematical Logic Quarterly. 2019 ; Vol. 65, No. 1. pp. 37-45.

BibTeX

@article{6516763c6c464cc68c47d16acc2564b3,

title = "Jump inversions of algebraic structures and Σ-definability",

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.).",

keywords = "THEOREM, REDUCIBILITY",

author = "Marat Faizrahmanov and Asher Kach and Iskander Kalimullin and Antonio Montalb{\'a}n and Vadim Puzarenko",

note = "Publisher Copyright: {\textcopyright} 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim",

year = "2019",

month = may,

day = "1",

doi = "10.1002/malq.201800015",

language = "English",

volume = "65",

pages = "37--45",

journal = "Mathematical Logic Quarterly",

issn = "0942-5616",

publisher = "Wiley-VCH Verlag",

number = "1",

}

RIS

TY - JOUR

T1 - Jump inversions of algebraic structures and Σ-definability

AU - Faizrahmanov, Marat

AU - Kach, Asher

AU - Kalimullin, Iskander

AU - Montalbán, Antonio

AU - Puzarenko, Vadim

PY - 2019/5/1

Y1 - 2019/5/1

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.).

KW - THEOREM

KW - REDUCIBILITY

UR - http://www.scopus.com/inward/record.url?scp=85065422390&partnerID=8YFLogxK

U2 - 10.1002/malq.201800015

DO - 10.1002/malq.201800015

M3 - Article

AN - SCOPUS:85065422390

VL - 65

SP - 37

EP - 45

JO - Mathematical Logic Quarterly

JF - Mathematical Logic Quarterly

SN - 0942-5616

IS - 1

ER -

ID: 20039318