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On Two Ways of Representation of Uncountable Structures. / Morozov, A. S.

In: Algebra and Logic, Vol. 64, No. 5, 11.2026, p. 330-348.

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

Harvard

Morozov, AS 2026, 'On Two Ways of Representation of Uncountable Structures', Algebra and Logic, vol. 64, no. 5, pp. 330-348. https://doi.org/10.1007/s10469-026-09838-0

APA

Morozov, A. S. (2026). On Two Ways of Representation of Uncountable Structures. Algebra and Logic, 64(5), 330-348. https://doi.org/10.1007/s10469-026-09838-0

Vancouver

Morozov AS. On Two Ways of Representation of Uncountable Structures. Algebra and Logic. 2026 Nov;64(5):330-348. doi: 10.1007/s10469-026-09838-0

Author

Morozov, A. S. / On Two Ways of Representation of Uncountable Structures. In: Algebra and Logic. 2026 ; Vol. 64, No. 5. pp. 330-348.

BibTeX

@article{c208865891264ccda9c16c4b9cfb5179,
title = "On Two Ways of Representation of Uncountable Structures",
abstract = "An embedding of the hereditarily finite superstructure over the ordered field of real numbers into the set of reals is constructed which takes Σ-subsets to sets computable by infinite time Blum-Shub-Smale machines (ITBMs). A notion of ITBM-constructivizable structure is introduced. It is proved that constructivizability of an arbitrary algebraic structure over the ordered field of real numbers implies its ITBM-constructivizability. We obtain a theorem on the existence of ITBM-constructivizable models of the cardinality of the continuum for countable consistent theories with infinite models.",
keywords = "ITBM-constructivizable structure, algebraic structure, hereditarily finite superstructure, infinite time Blum-Shub-Smale machines, ordered field of real numbers",
author = "Morozov, {A. S.}",
note = "Morozov, A.S. On Two Ways of Representation of Uncountable Structures. Algebra Logic 64, 330–348 (2025). https://doi.org/10.1007/s10469-026-09838-0 Supported by Russian Science Foundation, Project No. 23-11-00170, https://rscf.ru/project/23-11-00170/.",
year = "2026",
month = nov,
doi = "10.1007/s10469-026-09838-0",
language = "English",
volume = "64",
pages = "330--348",
journal = "Algebra and Logic",
issn = "0002-5232",
publisher = "Springer US",
number = "5",

}

RIS

TY - JOUR

T1 - On Two Ways of Representation of Uncountable Structures

AU - Morozov, A. S.

N1 - Morozov, A.S. On Two Ways of Representation of Uncountable Structures. Algebra Logic 64, 330–348 (2025). https://doi.org/10.1007/s10469-026-09838-0 Supported by Russian Science Foundation, Project No. 23-11-00170, https://rscf.ru/project/23-11-00170/.

PY - 2026/11

Y1 - 2026/11

N2 - An embedding of the hereditarily finite superstructure over the ordered field of real numbers into the set of reals is constructed which takes Σ-subsets to sets computable by infinite time Blum-Shub-Smale machines (ITBMs). A notion of ITBM-constructivizable structure is introduced. It is proved that constructivizability of an arbitrary algebraic structure over the ordered field of real numbers implies its ITBM-constructivizability. We obtain a theorem on the existence of ITBM-constructivizable models of the cardinality of the continuum for countable consistent theories with infinite models.

AB - An embedding of the hereditarily finite superstructure over the ordered field of real numbers into the set of reals is constructed which takes Σ-subsets to sets computable by infinite time Blum-Shub-Smale machines (ITBMs). A notion of ITBM-constructivizable structure is introduced. It is proved that constructivizability of an arbitrary algebraic structure over the ordered field of real numbers implies its ITBM-constructivizability. We obtain a theorem on the existence of ITBM-constructivizable models of the cardinality of the continuum for countable consistent theories with infinite models.

KW - ITBM-constructivizable structure

KW - algebraic structure

KW - hereditarily finite superstructure

KW - infinite time Blum-Shub-Smale machines

KW - ordered field of real numbers

UR - https://www.scopus.com/pages/publications/105046202688

UR - https://www.mendeley.com/catalogue/d317132a-0c4f-3292-a5ef-b74ad86c676f/

U2 - 10.1007/s10469-026-09838-0

DO - 10.1007/s10469-026-09838-0

M3 - Article

VL - 64

SP - 330

EP - 348

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 5

ER -

ID: 81651644