Economy of Descriptions and Minimal Indices

In Part One sets of minimal indices It is shown that M and Mare inmtune and s M and Mare defined.tftat M = ¢" M J. oin T ' s K =T ¢" .Subsets of M called~ and~ are defined and it is proved that ~ =T ¢ ' and that ~ =T If1M =T »lM =T ¢".Ms is relativized with respect to a set A of integers, and for any two sets A and B of integers such that A" s:T B' and any total function g :,;;T B" and a size function s s:T A the following set C is shown to be nonempty A B A c = {y I ax[W = W and x EKand sC however is empty for some total functions g s:T B"'.Various special cases are considered, e.g.WB in the definition of C i s restricted to be finite or a singleton.-V -