Scalable sets are defined and their properties studied, It is shown th
at the set of scalable sets is the isomorphism closure of the set of r
ankable sets and that every scalable set is P-isomorphic to some ranka
ble set. Scalable sets coincide with P-printable sets when sparse, and
with P-paddable sets when thick. Using scalability as a tool, the P-i
somorphism question for polynomial-time computable sets of similar den
sities is examined.