  By considering labeled configurations of ``bounded multiplicity'', one can
construct a functor that fits between homology and stable homotopy. Based on
previous work, we are able to give an equivalent description of this labeled
construction in terms of loop space functors and symmetric products. This
yields a direct generalization of the May-Milgram model for iterated loop
spaces, and answers questions of Carlsson and Milgram posed in the handbook. We
give a classifying space formulation of our results hence extending an older
result of Segal. We finally relate our labeled construction to a theory of Lesh
and give a generalization of a well-known theorem of Quillen, Barratt and
Priddy.
