21 citations · 23 across the 11 of their papers we have counts for
13 papers
The number of measures on very large measurable cardinals
Arthur W. Apter, Eyal Kaplan, Alejandro Poveda
We study the possible number of normal measures on a measurable cardinal in settings where inner model techniques are unavailable. Instead, we exploit consequences of the Ultrapowe…
Strongly compact cardinals and the continuum function
Arthur W. Apter, Stamatis Dimopoulos, Toshimichi Usuba
We study the general problem of the behaviour of the continuum function in the presence of non-supercompact strongly compact cardinals.
Singular cardinals and strong extenders
Arthur W. Apter, James Cummings, Joel David Hamkins
We investigate the circumstances under which there exist a singular cardinal and a short -extender witnessing " is -strong", such that is singular in $\Ul…
Consecutive singular cardinals and the continuum function
Arthur W. Apter, Brent Cody
We show that from a supercompact cardinal κ, there is a forcing extension V[G] that has a symmetric inner model N in which ZF + not AC holds, κ and κ^+ are both singular, and the c…
Inner models with large cardinal features usually obtained by forcing
Arthur Apter, Victoria Gitman, Joel David Hamkins
We construct a variety of inner models exhibiting features usually obtained by forcing over universes with large cardinals. For example, if there is a supercompact cardinal, then t…
Large cardinals with few measures
Arthur W. Apter, James Cummings, Joel David Hamkins
We show, assuming the consistency of one measurable cardinal, that it is consistent for there to be exactly kappa+ many normal measures on the least measurable cardinal kappa. This…