  It is known that the set of possible cofinalities $\mathrm{pcf}(A)$ has good
properties if $A$ is a progressive interval of regular cardinals. In this
paper, we give an interval of regular cardinals $A$ such that $\mathrm{pcf}(A)$
has no good properties in the presense of a measurable cardinal, or in generic
extensions by Prikry-type forcing.
