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Turing Degrees and Automorphism Groups of Substructure Lattices. / Dimitrov, R. D.; Harizanov, V.; Morozov, A. S.

In: Algebra and Logic, Vol. 59, No. 1, 01.03.2020, p. 18-32.

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

Harvard

Dimitrov, RD, Harizanov, V & Morozov, AS 2020, 'Turing Degrees and Automorphism Groups of Substructure Lattices', Algebra and Logic, vol. 59, no. 1, pp. 18-32. https://doi.org/10.1007/s10469-020-09576-x

APA

Dimitrov, R. D., Harizanov, V., & Morozov, A. S. (2020). Turing Degrees and Automorphism Groups of Substructure Lattices. Algebra and Logic, 59(1), 18-32. https://doi.org/10.1007/s10469-020-09576-x

Vancouver

Dimitrov RD, Harizanov V, Morozov AS. Turing Degrees and Automorphism Groups of Substructure Lattices. Algebra and Logic. 2020 Mar 1;59(1):18-32. doi: 10.1007/s10469-020-09576-x

Author

Dimitrov, R. D. ; Harizanov, V. ; Morozov, A. S. / Turing Degrees and Automorphism Groups of Substructure Lattices. In: Algebra and Logic. 2020 ; Vol. 59, No. 1. pp. 18-32.

BibTeX

@article{c706d857344e4ed9bb3294f6904eb0ec,
title = "Turing Degrees and Automorphism Groups of Substructure Lattices",
abstract = "The study of automorphisms of computable and other structures connects computability theory with classical group theory. Among the noncomputable countable structures, computably enumerable structures are one of the most important objects of investigation in computable model theory. Here we focus on the lattice structure of computably enumerable substructures of a given canonical computable structure. In particular, for a Turing degree d, we investigate the groups of d-computable automorphisms of the lattice of d-computably enumerable vector spaces, of the interval Boolean algebra Bη of the ordered set of rationals, and of the lattice of d-computably enumerable subalgebras of Bη. For these groups, we show that Turing reducibility can be used to substitute the group-theoretic embedding. We also prove that the Turing degree of the isomorphism types for these groups is the second Turing jump d′′ of d.",
keywords = "automorphism, groups of d-computable automorphisms, interval Boolean algebra of ordered set of rationals, lattice of d-enumerable vector subspaces, Turing degree, Turing jump, Turing reducibility",
author = "Dimitrov, {R. D.} and V. Harizanov and Morozov, {A. S.}",
note = "Publisher Copyright: {\textcopyright} 2020, Springer Science+Business Media, LLC, part of Springer Nature. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2020",
month = mar,
day = "1",
doi = "10.1007/s10469-020-09576-x",
language = "English",
volume = "59",
pages = "18--32",
journal = "Algebra and Logic",
issn = "0002-5232",
publisher = "Springer US",
number = "1",

}

RIS

TY - JOUR

T1 - Turing Degrees and Automorphism Groups of Substructure Lattices

AU - Dimitrov, R. D.

AU - Harizanov, V.

AU - Morozov, A. S.

N1 - Publisher Copyright: © 2020, Springer Science+Business Media, LLC, part of Springer Nature. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/3/1

Y1 - 2020/3/1

N2 - The study of automorphisms of computable and other structures connects computability theory with classical group theory. Among the noncomputable countable structures, computably enumerable structures are one of the most important objects of investigation in computable model theory. Here we focus on the lattice structure of computably enumerable substructures of a given canonical computable structure. In particular, for a Turing degree d, we investigate the groups of d-computable automorphisms of the lattice of d-computably enumerable vector spaces, of the interval Boolean algebra Bη of the ordered set of rationals, and of the lattice of d-computably enumerable subalgebras of Bη. For these groups, we show that Turing reducibility can be used to substitute the group-theoretic embedding. We also prove that the Turing degree of the isomorphism types for these groups is the second Turing jump d′′ of d.

AB - The study of automorphisms of computable and other structures connects computability theory with classical group theory. Among the noncomputable countable structures, computably enumerable structures are one of the most important objects of investigation in computable model theory. Here we focus on the lattice structure of computably enumerable substructures of a given canonical computable structure. In particular, for a Turing degree d, we investigate the groups of d-computable automorphisms of the lattice of d-computably enumerable vector spaces, of the interval Boolean algebra Bη of the ordered set of rationals, and of the lattice of d-computably enumerable subalgebras of Bη. For these groups, we show that Turing reducibility can be used to substitute the group-theoretic embedding. We also prove that the Turing degree of the isomorphism types for these groups is the second Turing jump d′′ of d.

KW - automorphism

KW - groups of d-computable automorphisms

KW - interval Boolean algebra of ordered set of rationals

KW - lattice of d-enumerable vector subspaces

KW - Turing degree

KW - Turing jump

KW - Turing reducibility

UR - http://www.scopus.com/inward/record.url?scp=85085048490&partnerID=8YFLogxK

UR - https://elibrary.ru/item.asp?id=42852429

U2 - 10.1007/s10469-020-09576-x

DO - 10.1007/s10469-020-09576-x

M3 - Article

AN - SCOPUS:85085048490

VL - 59

SP - 18

EP - 32

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 1

ER -

ID: 24391263