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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On the singular cardinal hypothesis


Author: W. J. Mitchell
Journal: Trans. Amer. Math. Soc. 329 (1992), 507-530
MSC: Primary 03E55; Secondary 03E35, 03E50
DOI: https://doi.org/10.1090/S0002-9947-1992-1073778-4
MathSciNet review: 1073778
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Abstract: We use core model theory to obtain the following lower bounds to the consistency strength for the failure of the Singular Cardinal Hypothesis: Suppose that $ \kappa $ is a singular strong limit cardinal such that $ {2^\kappa } > {\kappa ^ + }$. Then there is an inner model $ K$ such that $ o(\kappa ) = {\kappa ^{ + + }}$ in $ K$ if $ \kappa $ has uncountable cofinality, and $ \forall \alpha < \kappa \exists \nu < \kappa o(\kappa ) \geqslant \nu $ in $ K$ otherwise.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1992-1073778-4
Keywords: Core model, covering lemma, GCH, SCH
Article copyright: © Copyright 1992 American Mathematical Society

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