English

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

R2 v1 2026-07-22T16:32:45.776Z