Varsovian models I∗†

نویسندگان

  • Grigor Sargsyan
  • Ralf Schindler
چکیده

Let Msw denote the least iterable inner model with a strong cardinal above a Woodin cardinal. By [8], Msw has a fully iterable core model, K Msw , and Msw is thus the least iterable extender model which has an iterable core model with a Woodin cardinal. In V , KMsw is an iterate of Msw via its iteration strategy Σ. We here show that Msw has a bedrock which arises from K Msw by telling KMsw a specific fragment Σ̄ of its own iteration strategy, which in turn is a tail of Σ. Hence Msw is a generic extension of L[K Msw , Σ̄], but the latter model is not a generic extension of any inner model properly contained in it. These results generalize to models of the form Ms(x) for a cone of reals x, where Ms(x) denotes the least iterable inner model with a strong cardinal containing x. In particular, the least iterable inner model with a strong cardinal above two (or seven, or boundedly many) Woodin cardinals has a 2–small core model K with a Woodin cardinal and its bedrock is again of the form L[K, Σ̄].

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تاریخ انتشار 2016