0# and elementary end extensions of Vk
Amir Leshem
Abstract
In this paper we prove that if k is a cardinal in L[0#], then there is an inner model M such that M |= (Vk,E) has no elementary end extension. In particular if 0# exists then weak compactness is never downwards absolute. We complement the result with a lemma stating that any cardinal greater than aleph1 of uncountable cofinality in L[0#] is Mahlo in every strict inner model of L[0#].
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