Measure and category (or rather, their recursion-theoretical counterpa
rts) have been used in theoretical computer science to make precise th
e intuitive notion ''for most of the recursive sets'', We use the noti
ons of effective measure and category to discuss the relative sizes of
inferrible sets, and their complements. We find that inferable sets b
ecome large rather quickly in the standard hierarchies of learnability
. On the other hand, the complements of the learnable sets are all lar
ge. (C) 1998-Elsevier Science B.V. All rights reserved.