# Ultrapowers by extenders of potential premice

I have a problem with an argument in Fine structure and iteration trees by Mitchell and Steel. Let $E$ be a $(\kappa, \lambda)$-extender. Let $\dot E^{\mathcal{M}}$ the a unary predicate with is interpreted as the extender sequence at $\alpha$. Let $\dot F^{\mathcal{M}}$ be a 3-ary predicate interpreted as the weakly amenable coding of $E_{\alpha}$.

Mitchell and Steel define the ultrapower in the case $\mathcal{M}$ is active. In the first page in http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?handle=euclid.lnl/1235423433&view=body&content-type=pdf_1 there is case 1 where $\mu < \kappa$ ($\mu$ is the critical point of $\dot F^{\mathcal{M}}$).

The authors claim this directly implies that $g$ is constant almost everywhere ($g$ is defined a couple of line before the argument). I don't understand why that is so. Thanks for any help.

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FSIT?${}{}{}{}$ –  Asaf Karagila Oct 19 '12 at 4:54
Fine Structure and Iteration Trees, [MS] 1994 –  user33714 Oct 19 '12 at 5:04
You want to put a proper citation, not everyone reading this will be aware of that. –  Asaf Karagila Oct 19 '12 at 5:07
OK, I am editing this right now. Actually, looking a second time at it, I think I've got the answer I'm looking for. The above thing is true just by definition of an equivalence class in the ultrapower. If $\mu$ is less than $\kappa$ then nothing is moved by the embedding at the level of $\mu$ –  user33714 Oct 19 '12 at 5:11
If you have an answer you can post it as an answer to your own question. Give it a day or two for some feedback, and then accept it if you are certain it is correct. –  Asaf Karagila Oct 19 '12 at 5:18