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Abstract <p>We prove that there exists <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8284_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(2^{\omega}\)</EquationSource> <!--LobJMat2560611Morozov-m1--> </InlineEquation> non-<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8284_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Sigma\)</EquationSource> <!--LobJMat2560611Morozov-m2--> </InlineEquation>-isomorphic and (even pairwise non-<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8284_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Sigma\)</EquationSource> <!--LobJMat2560611Morozov-m3--> </InlineEquation>-embeddable) <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8284_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Sigma\)</EquationSource> <!--LobJMat2560611Morozov-m4--> </InlineEquation>-presentations of the additive group of the real numbers in the hereditarily finite superstructure over the ordered field of the real numbers.</p>

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On Presentations of the Addition over the Reals

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • A. S. Morozov

摘要

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.