In this paper we prove that from large cardinals it is consistent that there is a singular strong limit cardinal v such that the singular cardinal hypothesis fails at v and every collection of fewer than cf(v) stationary subsets of v+ reflects simultaneously. For cf(v) > ω, this situation was not previously known to be consistent. Using different methods, we reduce the upper bound on the consistency strength of this situation for cf(v) = ω to below a single partially supercompact cardinal. The previous upper bound of infinitely many supercompact cardinals was due to Sharon.
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