Full comprehension for sets is impossible. That is, there is no notion of set such that for every property of sets there is a set consisting of the sets having that property.

At: RussellsParadox Frege2

  (Set:Type, :(SetSetProp).
  (P:(SetProp). p:Set. x:Set. (x  p)  P(x))

1

1. Set : Type 2.  : SetSetProp 3. P:(SetProp). p:Set. x:Set. (x  p)  P(x)   False

5 steps

About: IF YOU CAN SEE THIS go to /sfa/Nuprl/Shared/Xindentation_hack_doc.html