Nonpresentability of Some Structures of Analysis in Hereditarily Finite Superstructures

A. S. Morozov

doi:10.1007/s10469-018-9468-7

Nonpresentability of Some Structures of Analysis in Hereditarily Finite Superstructures

A. S. Morozov

Section of Discrete Mathematics and Computer Science of MMD and SESC

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

2 Citations (Scopus)

Abstract

It is proved that any countable consistent theory with infinite models has a Σ-presentable model of cardinality 2^ω 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.

Original language	English
Pages (from-to)	458-472
Number of pages	15
Journal	Algebra and Logic
Volume	56
Issue number	6
DOIs	https://doi.org/10.1007/s10469-018-9468-7
Publication status	Published - 1 Jan 2018

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

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10.1007/s10469-018-9468-7

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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

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EP - 472

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 6

ER -

Nonpresentability of Some Structures of Analysis in Hereditarily Finite Superstructures

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Keywords

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