# Sh:963

• Cummings, J., Džamonja, M., Magidor, M., Morgan, C., & Shelah, S. (2017). A framework for forcing constructions at successors of singular cardinals. Trans. Amer. Math. Soc., 369(10), 7405–7441.
• Abstract:
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 \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.

• published version (37p)
Bib entry
@article{Sh:963,
author = {Cummings, James and D{\v{z}}amonja, Mirna and Magidor, Menachem and Morgan, Charles and Shelah, Saharon},
title = {{A framework for forcing constructions at successors of singular cardinals}},
journal = {Trans. Amer. Math. Soc.},
fjournal = {Transactions of the American Mathematical Society},
volume = {369},
number = {10},
year = {2017},
pages = {7405--7441},
issn = {0002-9947},
mrnumber = {3683113},
mrclass = {03E35 (03E55 03E75)},
doi = {10.1090/tran/6974},
note = {\href{https://arxiv.org/abs/1403.6795}{arXiv: 1403.6795}},
arxiv_number = {1403.6795}
}