PFA and complemented subspaces of ℓ_∞/c₀

Alan Dow

Section 2 of the paper starts: Let A_n, n ∈ ℕ be a partition of ℕ into infinite sets. Here we prove formally that there exists a partition of ℕ into infinitely many infinite sets. The idea is to use the 2-adic valuation. (We first prove it for just two sets as a warmup.)

We also introduce the ideals A⊥ and I (introduced on page 2 of the paper) and prove A⊥ ⊆ I.