• A. W. Apter, J. Cummings, and J. D. Hamkins, “Singular cardinals and strong extenders,” Central European Journal of Mathematics. (to appear)  
  Citation arχiv

  @ARTICLE{ApterCummingsHamkins:SingularCardinalsAndStrongExtenders,
  author = {Arthur W. Apter and James Cummings and Joel David Hamkins},
  title = {Singular cardinals and strong extenders},
  journal = {Central European Journal of Mathematics},
  year = {},
  volume = {},
  number = {},
  pages = {},
  month = {},
  url = {http://arxiv.org/abs/1206.3703},
  eprint = {1206.3703},
  note = {to appear},
  abstract = {},
  keywords = {},
  source = {},
  }

Brent Cody asked the question whether the situation can arise that one has an elementary embedding $j:V\to M$ witnessing the $\theta$-strongness of a cardinal $\kappa$, but where $\theta$ is regular in $M$ and singular in $V$.

In this article, we investigate the various circumstances in which this does and does not happen, the circumstances under which there exist a singular cardinal $\mu$ and a short $(\kappa, \mu)$-extender $E$ witnessing “$\kappa$ is $\mu$-strong”, such that $\mu$ is singular in $Ult(V, E)$.