if 0 holds in v, then there is a closed unbounded class of ordinals that are indiscernible in l. while some of these are not even initial ordinals in v, they have all the large cardinal properties weaker than 0 in l. furthermore, any strictly increasing class function from the class of indiscernibles to itself can be extended in a unique way to an elementary embedding of l into l. this gives l a nice structure of repeating segments.