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Algebra Logika, 2017, Volume 56, Number 6, Pages 691–711 (Mi al825)  

This article is cited in 1 scientific paper (total in 1 paper)

Nonpresentability of some structures of analysis in hereditarily finite superstructures

A. S. Morozovab

a Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090 Russia
b Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090 Russia

Abstract: It is proved that any countable consistent theory with infinite models has a $\Sigma$-presentable model of cardinality $2^\omega$ over $\mathbb{HF(R})$. 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 $\Sigma$-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: $\Sigma$-presentability, countable consistent theory, hereditarily finite superstructure, existentially Steinitz structure, semigroup of continuous functions, nonstandard analysis, infinite-dimensional separable Hilbert space.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00376
13-01-91001-АНФ-а
Supported by RFBR, projects No. 14-01-00376 and 13-01-91001-ANF-a.


DOI: https://doi.org/10.17377/alglog.2017.56.604

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English version:
Algebra and Logic, 2018, 56:6, 458–472

Bibliographic databases:

UDC: 510.65
Received: 09.03.2017
Revised: 14.09.2017

Citation: A. S. Morozov, “Nonpresentability of some structures of analysis in hereditarily finite superstructures”, Algebra Logika, 56:6 (2017), 691–711; Algebra and Logic, 56:6 (2018), 458–472

Citation in format AMSBIB
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\by A.~S.~Morozov
\paper Nonpresentability of some structures of analysis in hereditarily finite superstructures
\jour Algebra Logika
\yr 2017
\vol 56
\issue 6
\pages 691--711
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\crossref{https://doi.org/10.17377/alglog.2017.56.604}
\transl
\jour Algebra and Logic
\yr 2018
\vol 56
\issue 6
\pages 458--472
\crossref{https://doi.org/10.1007/s10469-018-9468-7}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Morozov A.S., “Computable Model Theory Over the Reals”, Computability and Complexity: Essays Dedicated to Rodney G. Downey on the Occasion of His 60Th Birthday, Lecture Notes in Computer Science, 10010, eds. Day A., Fellows M., Greenberg N., Khoussainov B., Melnikov A., Rosamond F., Springer International Publishing Ag, 2017, 354–365  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и логика Algebra and Logic
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