Weak extender models are inner models for large cardinals for which the large cardinal notion is witnessed to hold by extenders from V. Weak-extender models generalize L[U].

Any weak extender model for supercompactness is necessarily universal for any large cardinal notion which can be formulated in terms of extenders. This suggests there is an ultimate version of L and this is Ultimate-L

Inner model theory currently involves two basic forms of inner models. These are extender models and strategic-extender models. The prospect of an ultimate L then leads to the question of which form should ultimate L take. Is it an extender model or a strategic-extender model? Or perhaps there are two versions of ultimate L.

We discuss evidence that there is only one version of ultimate L and we discuss other constraints which explain the ω-barrier.