  We generalize results of Gitik, Dzamonja-Shelah, and Magidor-Sinapova on the
existence of pseudo-Prikry sequences, which are sequences that approximate the
behavior of the generic objects introduced by Prikry-type forcings, in outer
models of set theory. Such sequences play an important role in the study of
singular cardinal combinatorics by placing restrictions on the type of behavior
that can consistently be obtained in outer models. In addition, we provide
results about the existence of diagonal pseudo-Prikry sequences, which
approximate the behavior of the generic objects introduced by diagonal
Prikry-type forcings. Our proof techniques are substantially different from
those of previous results and rely on an analysis of PCF-theoretic objects in
the outer model.
