Rudin-Keisler capturing and Mutual Stationairy at successors of Singulars

We introduce a combinatorial notion of measures called Rudin-Keisler capturing and use it to give a new construction of elementary substructures around singular cardinals. The new construction is used to establish mutual stationary results at the first successor of singular cardinals $⟨{\mathrm{\aleph }}_{\omega n+1}{⟩}_{n<\omega }$.