Let L[E] be an
iterable tame extender model.
We analyze to which extent L[E]
knows fragments of its own iteration strategy.
Specifically, we prove that inside L[E], for every cardinal
κ which is not a limit of Woodin cardinals
there is some cutpoint t < κ such that
Jκ[E] is iterable above t with respect to iteration trees
of length less than κ.
As an application we show
L[E] to be a model of the following two
cardinals versions of the diamond principle.
If λ > κ > ω₁ are cardinals, then
◇κ,λ* holds true,
and
if in addition λ is regular, then
◇κ,λ⁺ holds true.
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