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Universal graphs between a strong limit singular and its power.

Bibliographic Details
Title: Universal graphs between a strong limit singular and its power.
Authors: Poór, Márk, Shelah, Saharon
Source: Transactions of the American Mathematical Society; May2026, Vol. 379 Issue 5, p3111-3159, 49p
Subject Terms: Forcing (Model theory), Set theory, Continuum hypothesis
Abstract: The paper settles the problem of the consistency of the existence of a single universal graph between a strong limit singular and its power. Assuming that in a model of \mathbf {GCH} \kappa is supercompact and the cardinals \theta < \kappa, \lambda > \kappa are regular, as an application of a more general method, we obtain a forcing extension in which cf(\kappa) = \theta, the Singular Cardinal Hypothesis fails at \kappa and there exists a universal graph at cardinality \lambda \in (\kappa,2^\kappa). [ABSTRACT FROM AUTHOR]
Copyright of Transactions of the American Mathematical Society is the property of American Mathematical Society and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Universal graphs between a strong limit singular and its power.
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  Data: Transactions of the American Mathematical Society; May2026, Vol. 379 Issue 5, p3111-3159, 49p
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  Data: &lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Forcing+%28Model+theory%29%22&quot;&gt;Forcing (Model theory)&lt;/searchLink&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Set+theory%22&quot;&gt;Set theory&lt;/searchLink&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Continuum+hypothesis%22&quot;&gt;Continuum hypothesis&lt;/searchLink&gt;
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  Data: The paper settles the problem of the consistency of the existence of a single universal graph between a strong limit singular and its power. Assuming that in a model of \mathbf {GCH} \kappa is supercompact and the cardinals \theta &lt; \kappa, \lambda &gt; \kappa are regular, as an application of a more general method, we obtain a forcing extension in which cf(\kappa) = \theta, the Singular Cardinal Hypothesis fails at \kappa and there exists a universal graph at cardinality \lambda \in (\kappa,2^\kappa). [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label:
  Group: Ab
  Data: &lt;i&gt;Copyright of Transactions of the American Mathematical Society is the property of American Mathematical Society and its content may not be copied or emailed to multiple sites without the copyright holder&#39;s express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.&lt;/i&gt; (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1090/tran/9412
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      – Code: eng
        Text: English
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        PageCount: 49
        StartPage: 3111
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        Type: general
      – SubjectFull: Set theory
        Type: general
      – SubjectFull: Continuum hypothesis
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      – TitleFull: Universal graphs between a strong limit singular and its power.
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            NameFull: Poór, Márk
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            NameFull: Shelah, Saharon
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            – D: 01
              M: 05
              Text: May2026
              Type: published
              Y: 2026
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              Value: 379
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              Value: 5
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