  Usual math sets have special types: countable, compact, open, occasionally
Borel, rarely projective, etc. They have finite "depth": are described by a
single Set Theory formula with variables ranging over objects unrelated to math
formulas. Exotic expressions referring to sets with no depth limit or to
Powerset axiom appear mostly in esoteric or foundational studies. Recognizing
internal to math (formula-specified) and external (based on parameters in those
formulas) aspects of math objects greatly simplifies foundations. I postulate
external sets (not internally specified, treated as the domain of variables) to
be hereditarily countable and independent of formula-defined classes, i.e. with
finite Kolmogorov Information about them. This allows elimination of all
non-integer quantifiers in Set Theory statements.
