On Singular Stationarity I (mutual stationarity and ideal-based methods)

We study several ideal-based constructions in the context of singular stationarity. By combining methods of strong ideals, supercompact embeddings, and Prikry-type posets, we obtain three consistency results concerning mutually stationary sets, and answer a question of Foreman and Magidor concerning stationary sequences on the first uncountable cardinals, ${\mathrm{\aleph }}_n$, $1 \leq n < \omega$.