 In evaluating Rédei’s argument it is important to ask what counts as a physical thing. Einstein mentioned two possible candidates: bodies and fields.  Howard’s separability principle  permits a natural transposition of Einstein’s  real state separability principle  to field theory. Entangled states in AQFT violate section 5’s  state separability  principle just as they do in nonrelativistic quantum mechanics even though the split property and related independence conditions on their algebras hold. So if the content of a space-time region were specified by its algebra in AQFT, considered as a physical system with real physical state given by a state on that algebra, then Howard’s separability principle would fail. (Although the failure of the split property or other algebraic independence conditions for certain regions in a quantum field theory would represent a more radical threat to the separate existence of such physical systems in those regions than mere entanglement). But it is doubtful that Einstein would have counted observables or their algebras as physical things. If instead these are taken to represent magnitudes of physical fields or the spatio-temporal region on which they are defined then meeting Rédei’s Independence requirement is still consistent with failure of Howard’s (stronger) separability principle. Finally meeting Rédei’s operational separability condition only for non-selective operations would not suffice to ensure conformity to Local Action. Einstein’s reasons for rejecting the completeness of quantum mechanical description are naturally extended to AQFT: if a state on its local algebra completely specifies the real state of a space-time region then either the natural extension of his  real state separability principle  or his principle of  Local Action  fails.