Editing Covering lemma (section)

==Extenders and indiscernibles==
For core models without overlapping total extenders, the systems of indiscernibles are well understood.  Although (if K has an inaccessible limit of measurable cardinals), the system may depend on the set to be covered, it is well-determined and unique in a weaker sense.  One application of the covering is counting the number of (sequences of) indiscernibles, which gives optimal lower bounds for various failures of the [[singular cardinals hypothesis]].  For example, if K does not have overlapping total extenders, and κ is singular strong limit, and 2<sup>κ</sup>&nbsp;=&nbsp;κ<sup>++</sup>, then κ has Mitchell order at least κ<sup>++</sup> in&nbsp;K.  Conversely, a failure of the singular cardinal hypothesis can be obtained (in a generic extension) from κ with o(κ)&nbsp;=&nbsp;κ<sup>++</sup>.

For core models with overlapping total extenders (that is with a cardinal strong up to a measurable one), the systems of indiscernibles are poorly understood, and applications (such as the weak covering) tend to avoid rather than analyze the indiscernibles.