On the characterization of models of H

We give a characterization, with respect to a large class of models of untyped λ-calculus, of those models that are fully abstract for head-normalization, i.e., whose equational theory is H*. An extensional K-model D is fully abstract if and only if it is hyperimmune, i.e., non-well founded chains of elements of D cannot be captured by any recursive function.