A weak DoddóJensen lemma


Itay Neeman and John Steel





We show that every sufficiently iterable countable mouse has

a unique iteration strategy whose associated iteration maps

are lexicographically minimal. This enables us to extend the

results of [E. Schimmerling and J.R. Steel, Fine Structure

for tame inner models, J. of Symb. Logic vol. 61, pp. 621ó639]

on the good behavior of the standard parameter from tame mice

to arbitrary mice.