Standard

Nonpresentability of Some Structures of Analysis in Hereditarily Finite Superstructures. / Morozov, A. S.

In: Algebra and Logic, Vol. 56, No. 6, 01.01.2018, p. 458-472.

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

Harvard

Morozov, AS 2018, 'Nonpresentability of Some Structures of Analysis in Hereditarily Finite Superstructures', Algebra and Logic, vol. 56, no. 6, pp. 458-472. https://doi.org/10.1007/s10469-018-9468-7

APA

Morozov, A. S. (2018). Nonpresentability of Some Structures of Analysis in Hereditarily Finite Superstructures. Algebra and Logic, 56(6), 458-472. https://doi.org/10.1007/s10469-018-9468-7

Vancouver

Morozov AS. Nonpresentability of Some Structures of Analysis in Hereditarily Finite Superstructures. Algebra and Logic. 2018 Jan 1;56(6):458-472. doi: 10.1007/s10469-018-9468-7

Author

Morozov, A. S. / Nonpresentability of Some Structures of Analysis in Hereditarily Finite Superstructures. In: Algebra and Logic. 2018 ; Vol. 56, No. 6. pp. 458-472.

BibTeX

@article{ab9beffa1df448df99145a71eb4674f0,
title = "Nonpresentability of Some Structures of Analysis in Hereditarily Finite Superstructures",
abstract = "It is proved that any countable consistent theory with infinite models has a Σ-presentable model of cardinality 2ω over. It is shown that some structures studied in analysis (in particular, a semigroup of continuous functions, certain structures of nonstandard analysis, and infinite-dimensional separable Hilbert spaces) have no simple Σ-presentations in hereditarily finite superstructures over existentially Steinitz structures. The results are proved by a unified method on the basis of a new general sufficient condition.",
keywords = "countable consistent theory, existentially Steinitz structure, hereditarily finite superstructure, infinitedimensional separable Hilbert space, nonstandard analysis, semigroup of continuous functions, Σ-presentability, Sigma-presentability, MODELS, infinite-dimensional separable Hilbert space",
author = "Morozov, {A. S.}",
year = "2018",
month = jan,
day = "1",
doi = "10.1007/s10469-018-9468-7",
language = "English",
volume = "56",
pages = "458--472",
journal = "Algebra and Logic",
issn = "0002-5232",
publisher = "Springer US",
number = "6",

}

RIS

TY - JOUR

T1 - Nonpresentability of Some Structures of Analysis in Hereditarily Finite Superstructures

AU - Morozov, A. S.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - It is proved that any countable consistent theory with infinite models has a Σ-presentable model of cardinality 2ω over. It is shown that some structures studied in analysis (in particular, a semigroup of continuous functions, certain structures of nonstandard analysis, and infinite-dimensional separable Hilbert spaces) have no simple Σ-presentations in hereditarily finite superstructures over existentially Steinitz structures. The results are proved by a unified method on the basis of a new general sufficient condition.

AB - It is proved that any countable consistent theory with infinite models has a Σ-presentable model of cardinality 2ω over. It is shown that some structures studied in analysis (in particular, a semigroup of continuous functions, certain structures of nonstandard analysis, and infinite-dimensional separable Hilbert spaces) have no simple Σ-presentations in hereditarily finite superstructures over existentially Steinitz structures. The results are proved by a unified method on the basis of a new general sufficient condition.

KW - countable consistent theory

KW - existentially Steinitz structure

KW - hereditarily finite superstructure

KW - infinitedimensional separable Hilbert space

KW - nonstandard analysis

KW - semigroup of continuous functions

KW - Σ-presentability

KW - Sigma-presentability

KW - MODELS

KW - infinite-dimensional separable Hilbert space

UR - http://www.scopus.com/inward/record.url?scp=85042438199&partnerID=8YFLogxK

U2 - 10.1007/s10469-018-9468-7

DO - 10.1007/s10469-018-9468-7

M3 - Article

AN - SCOPUS:85042438199

VL - 56

SP - 458

EP - 472

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 6

ER -

ID: 10354307