Generic embeddings associated to an indestructibly weakly compact cardinal

I use generic embeddings induced by generic normal measures on Pκ(λ) that can be forced to exist if κ is an indestructibly weakly compact cardinal. These embeddings can be used in order to obtain the forcing axioms MA(<μ-closed) in forcing extensions. This has consequences in V: The singular cardinal hypothesis holds above κ, and κ has a useful Jónsson-like property. This, in turn, implies that the countable tower Q<κ works much like it does when κ is a Woodin limit of Woodin cardinals. One consequence is that every set of reals in the Chang model satisfies the regularity properties. So indestructibly weak compactness has effects on the cardinal arithmetic high up and also on the structure of the sets of real numbers, down low, similar to supercompactness.