On Presentations of the Addition over the Reals

We prove that there exists $$2^{\omega}$$ non- $$\Sigma$$ -isomorphic and (even pairwise non- $$\Sigma$$ -embeddable) $$\Sigma$$ -presentations of the additive group of the real numbers in the hereditarily finite superstructure over the ordered field of the real numbers.

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Publication Details

Journal
Lobachevskii Journal of Mathematics
Published
2025-04-01
DOI
https://doi.org/10.1134/s1995080225606113
Primary Topic
Computability, Logic, AI Algorithms
Type
article
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article

On Presentations of the Addition over the Reals

Andrey Morozov
Lobachevskii Journal of Mathematics
Computability, Logic, AI Algorithms
article

On Presentations of the Addition over the Reals

Andrey Morozov
article en

Abstract

We prove that there exists $$2^{\omega}$$ non- $$\Sigma$$ -isomorphic and (even pairwise non- $$\Sigma$$ -embeddable) $$\Sigma$$ -presentations of the additive group of the real numbers in the hereditarily finite superstructure over the ordered field of the real numbers.

Lobachevskii Journal of MathematicsVol. 46(4)
Novosibirsk State University (RU), Sobolev Institute of Mathematics (RU), Siberian Branch of the Russian Academy of Sciences (RU)
Openalex Percentile: Top 77%
Computability, Logic, AI Algorithms
DOISourceOpenAlex
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