Chapter 32: The Profinite Boundary Ring Z

the relevant chapter introduced the boundary local ring on omega-tails with stagewise addition and multiplication. This chapter extends that local structure to the full profinite ring ℤ_τ, the inverse limit of all finite quotient rings ℤ/M_k (where M_k is the kth primorial). The resulting ring is compact, totally disconnected, and isomorphic to the product of all p-adic integer rings. It encodes all the boundary data that omega-germs carry about the approach to ω.