Nonpresentability of Some Structures of Analysis in Hereditarily Finite Superstructures

Nonpresentability of Some Structures of Analysis in Hereditarily Finite Superstructures Full article

Journal

Algebra and Logic
ISSN: 0002-5232 , E-ISSN: 1573-8302

Output data

Year: 2018, Volume: 56, Number: 6, Pages: 458-472 Pages count : 15 DOI: 10.1007/s10469-018-9468-7

Tags

countable consistent theory; existentially Steinitz structure; hereditarily finite superstructure; infinitedimensional separable Hilbert space; nonstandard analysis; semigroup of continuous functions; Σ-presentability

Authors

Morozov A.S. ^1,2

Affiliations

1	Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russian Federation
2	Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russian Federation

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. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

Morozov A.S.
Nonpresentability of Some Structures of Analysis in Hereditarily Finite Superstructures
Algebra and Logic. 2018. V.56. N6. P.458-472. DOI: 10.1007/s10469-018-9468-7 WOS Scopus OpenAlex

Морозов А.С.
Непредставимость некоторых структур анализа в наследственно конечных надстройках
Алгебра и логика. 2017. Т.56. №6. С.691-711. DOI: 10.17377/alglog.2017.56.604 РИНЦ MathNet

Web of science:	WOS:000426390500004
Scopus:	2-s2.0-85042438199
OpenAlex:	W2791425253

DB	Citing
Scopus	2
OpenAlex	4
Web of science	2