Design a sequence S₀, S₁, ... , S_∞ where each S_i
   1) is a string of characters from the set
      {φ, "right brace", "left brace", comma} (φ denotes the empty set),
   2) denotes a valid set, and
   3) |S_i| = i.

For clarity you can define substrings and use recursion.

Note; S_i = {φ,{φ},{φ},φ,{φ,{φ}}} = {φ,{φ},{φ,{φ}}}
                |S_i| = 3 not |S_i| = 5.

Note: φ = {}. I don't know if this will help.

A possible start: S₀ = φ , S₁ = {φ} , ...