 Summing up, upon first inspection the levels \(\Sigma^1_n\) and \(\Pi^1_n\) of the hierarchy of second-order formulas grow strictly in expressive power as n increases, but a more careful analysis reveals that already the first level \(\Sigma^1_1\cup \Pi^1_1\) has the power of all the levels \(\Sigma^1_n, \Pi^1_n\) even if the power is somewhat implicit and needs to be brought to light.