  Large cardinals arising from the existence of arbitrarily long end elementary
extension chains over models of set theory are studied here. In particular, we
show that the large cardinals obtained that way (`Unfoldable cardinals') behave
as a `boundary' between properties consistent with `V=L' and existence of
indiscernibles. We also provide an `embedding characterisation' of the
unfoldable cardinals and study their preservation and destruction by various
different forcings.
