A framework for forcing constructions at successors of singular cardinals

A framework for forcing constructions at successors of singular cardinals

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 \kappa of uncountable cofinality where SCH fails and such that there is a collection of size less than 2^{\kappa ^+} of graphs on \kappa ^+ such th...

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Veröffentlicht in:Transactions of the American Mathematical Society 2017-10, Vol.369 (10), p.7405-7441
Hauptverfasser: Cummings, James, Džamonja, Mirna, Magidor, Menachem, Morgan, Charles, Shelah, Saharon
Format: Artikel
Sprache:eng
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Zusammenfassung: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 \kappa of uncountable cofinality where SCH fails and such that there is a collection of size less than 2^{\kappa ^+} of graphs on \kappa ^+ such that any graph on \kappa ^+ embeds into one of the graphs in the collection.]]>
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/6974