0# and inner models
Copyright policy )0# and inner models
In this paper we examine the cardinal structure of inner models that satisfy GCH but do not contain 0#. We show, assuming that 0# exists, that such models necessarily contain Mahlo cardinals of high order, but without further assumptions need not contain a cardinal κ which is κ-Mahlo. The principal tools are the Covering Theorem for L and the technique of reverse Easton iteration.Let I denote the class of Silver indiscernibles for L and 〈iα ∣ α ϵ ORD〉 its increasing enumeration. Also fix an inner model M of GCH not containing 0# and let ωα denote the ωα of the model M[0#], the least inner model containing M as a submodel and 0# as an element.
Large cardinals, Inner models, including constructibility, ordinal definability, and core models, inner models, Consistency and independence results, Mahlo cardinals, 0 sharp
Large cardinals, Inner models, including constructibility, ordinal definability, and core models, inner models, Consistency and independence results, Mahlo cardinals, 0 sharp
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