  In this paper we study admissible extensions of several theories T of reverse
mathematics. The idea is that in such an extension the structure M = (N,S,\in)
of the natural numbers N and collection of sets of natural numbers S has to
obey the axioms of T while simultaneously one also has a set-theoretic world
with transfinite levels erected on top of M governed by the axioms of
Kripke-Platek set theory, KP.
