Scalability and the Isomorphism Problem

Scalable sets are de ned and their properties studied. It is shown that the set of scalable sets is the isomorphism closure of the set of rankable sets and that every scalable set is P-isomorphic to some rankable set. Scalable sets coincide with P-printable sets when sparse, and with P-paddable sets when thick. Using scalability as a tool, the P-isomorphism question for polynomial-time computable sets of similar densities is examined.