Abstract

Journal of Mathematical Logic, Ahead of Print. We introduce a new compactness principle which we call the gluing property. For a measurable cardinal [math] and a cardinal [math], we say that [math] has the [math]-gluing property if every sequence of [math]-many [math]-complete ultrafilters on [math] can be glued into an extender. We show that every [math]-compact cardinal has the [math]-gluing property, yet non-necessarily the [math]-gluing property. Finally, we compute the exact consistency strength for [math] to have the [math]-gluing property — this being [math].