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gaps as derived models and correctness of mice
Assume ZF + AD + V=L(R). Let be a gap with
admissible. We analyze as a natural form of
``derived model'' of a premouse , where is found in a generic extension
of . In particular, we will have , and if ``
exists'', then and in fact have the same universe. This
analysis will be employed in further work, yet to appear, toward a resolution
of a conjecture of Rudominer and Steel on the nature of , for
-small mice . We also establish some preliminary work toward this
conjecture in the present paper.Comment: 128 page