A framework for forcing constructions at successors of singular cardinals

Cummings, James, Dzamonja, Mirna, Magidor, Menachem, Morgan, Charles and Shelah, Saharon (2017) A framework for forcing constructions at successors of singular cardinals. Transactions of the American Mathematical Society, 369 (10). pp. 7405-7441. ISSN 0002-9947

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We describe a framework for proving consistency results about singular cardinals of arbitrary cofinality and their successors. This framework allows the construction of models in which the Singular Cardinals Hypothesis fails at a singular cardinal κ of uncountable cofinality, while κ^+ enjoys various combinatorial properties. As a sample application, we prove the consistency (relative to that of ZFC plus a supercompact cardinal) of there being a strong limit singular cardinal κ of uncountable cofinality where SCH fails and such that there is a collection of size less than 2^{κ^+} of graphs on κ^+ such that any graph on κ^+ embeds into one of the graphs in the collection.

Item Type: Article
Uncontrolled Keywords: successor of singular cardinal,iterated forcing ,strong chain condition,radin forcing forcing axiom,universal graph,indestructible supercompat cardinal
Faculty \ School: Faculty of Science > School of Mathematics
UEA Research Groups: Faculty of Science > Research Groups > Logic
Depositing User: Pure Connector
Date Deposited: 18 May 2016 13:00
Last Modified: 22 Oct 2022 01:07
URI: https://ueaeprints.uea.ac.uk/id/eprint/58863
DOI: 10.1090/tran/6974

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