0^# and elementary end extensions of V_k

Details 0^# and elementary end extensions of V_k 0^# and elementary end extensions of V_k

2000-05-17

arxiv.org/abs/math/0005175v1

Mathematics

Logic

To appear in Proc. of the AMS

Scientific paper

In this paper we prove that if k is a cardinal in L[0^#], then there is an inner model M such that M |= (V_k,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 aleph_1 of uncountable cofinality in L[0^#] is Mahlo in every strict inner model of L[0^#].

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