On the singular cardinal hypothesis
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- by W. J. Mitchell PDF
- Trans. Amer. Math. Soc. 329 (1992), 507-530 Request permission
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.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- 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