  The following table indicates what happens with repeated applications of the revision rule τM to the hypothesis h0 from Example 3.1. For each ordinal η, we will indicate the ηth hypothesis by Sη (suppressing the index M on τ). Thus S0 = h0, S1 = τ(h0), S2 = τ2(h0), S3 = τ3(h0), and Sω, the ωth hypothesis, is determined in some way from the hypotheses leading up to it. So, starting with h0 from Example 3.3, our revision sequence begins as follows: 