Appears in collections : 14th International workshop in set theory / XIVe Atelier international de théorie des ensembles, Exposés de recherche

We will analyze consequences of various types of Prikry forcing on combinatorial properties at singular cardinals and their successors, focusing on weak square and simultaneous stationary reflection. The motivation is how much compactness type properties can be obtained at successors of singulars, and especially the combinatorics at $\aleph_{\omega+1}$.