TITLE: Radin generics from iterated ultrapowers
QUESTION [5 upvotes]: Let $u$ be a measure sequence derived from some embedding $j:V\rightarrow M$. I heard that from iterating $j$ is possible to define a generic filter for some Radin forcing $\mathbb{R}_w$. Specifically, $\mathbb{R}_w$ is the Radin forcing defined using the measure sequence $w=j_{\alpha}(u)$, where $j_\alpha$ is the $\alpha^{th}$-iterated of $j$.
My question is the following: Which are the measures that we use to carry out this process? Are the second coordinates (i.e. $u_\gamma(1)$) of the corresponding measure sequence $u_\gamma$? Are the whole measure sequences $u_\gamma$? In this latter case, how looks like the definition of a ultrapower given by a measure sequence $u_\gamma$?

REPLY [4 votes]: See section 5 (called "Generating generic sequences by iterating j") of Radin's paper Adding closed cofinal sequences to large cardinals.
More details: The iteration is the usual one, using $j$ (see my comment below). Now the point is that is $u$ is the measure sequence in $V$, then there is $\sigma: ORD \to V$ so that $\sigma(\alpha)=j_{0, \alpha}(u)\restriction \beta_\alpha,$ for some suitable $\beta_\alpha$ and such that for any $\alpha, \sigma \restriction \alpha+1$ is $\mathbb{R}_{\sigma(\alpha)}$-generic over $M_\alpha$.