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On the singular cardinal hypothesis

Mitchell, W. J. (1992) On the singular cardinal hypothesis. Transactions of the American Mathematical Society, 329 (2). pp. 507-530. ISSN 0002-9947. doi:10.1090/S0002-9947-1992-1073778-4.

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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 κ is a singular strong limit cardinal such that 2^K > κ^+. Then there is an inner model K such that o(k) = κ^(++) in K if κ has uncountable cofinality, and ∀α < κ∃ν < κ o(κ) ≥ ν in K otherwise.

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Additional Information:© 1992 American Mathematical Society. Received by the editors March 27, 1990. Some of the work in this paper was done while the author was visiting the Hebrew University with support from the Lady Davis Foundation, and while the author was visiting UCLA and the California Institute of Technology. This work was partially supported by grant number MS-8614447 from the National Science Foundation. I would like to thank the referee for a careful reading of this paper and many helpful suggestions.
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Lady Davis FoundationUNSPECIFIED
Subject Keywords:Core model, covering lemma, GCH, SCH
Issue or Number:2
Classification Code:1980 Mathematics Subject Classification (1985 Revision). Primary 03E35, 03E45, 03E55
Record Number:CaltechAUTHORS:20170408-162417299
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:76178
Deposited By: 1Science Import
Deposited On:09 Aug 2017 21:59
Last Modified:15 Nov 2021 16:58

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