IV.D249 — Refinement Tower mathcalR

The refinement tower R = (alpha_n, rho_n)_{n >= 1} with alpha_n := rho^{n-1}(alpha) and transition maps rho_n : alpha_n -> alpha_{n+1}. A directed system forming a chain alpha_1 -> alpha_2 -> ... encoding all levels of the progression operator applied to the seed generator alpha.