0^# and elementary end extensions of V_k
Logic
2007-05-23 v1
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 |= (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^#].
Cite
@article{arxiv.math/0005175,
title = {0^# and elementary end extensions of V_k},
author = {Amir Leshem},
journal= {arXiv preprint arXiv:math/0005175},
year = {2007}
}
Comments
To appear in Proc. of the AMS