Condensation For Mouse Pairs

Source abstract

This is the first of two papers on the fine structure of HOD in models of the Axiom of Determinacy ([Formula: see text]). Let [Formula: see text]. [12] shows that under a natural hypothesis on the existence of iteration strategies, the basic fine structure theory for pure extender models goes over to [Formula: see text]. In this paper, we prove a fine condensation theorem, quite similar to Theorem 9.3.2 of Zeman’s book [18], except that condensation for iteration strategies has been added to the mix. In the second paper [15], we use this theorem to analyze and prove basic facts about the Dodd parameters for lbr hod mice. The results of these two papers will be used to show that in [Formula: see text], [Formula: see text] holds iff [Formula: see text] is not subcompact.