A FRAMEWORK FOR FORCING CONSTRUCTIONS AT SUCCESSORS OF SINGULAR CARDINALS

作者：Cummings James^*; Dzamonja Mirna; Magidor Menachem; Morgan Charles; Shelah Saharon

来源：Transactions of the American Mathematical Society, 2017, 369(10): 7405-7441.

DOI：10.1090/tran/6974

• Successor of singular cardinal
• iterated forcing
• strong chain condition
• Radin forcing
• forcing axiom
• universal graph
• indestructible supercompact cardinal

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 kappa of uncountable cofinality, while kappa(+) 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. 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.

• 出版日期2017-10
• 单位rutgers